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Large sample techniques for statistics / / Jiming Jiang
| Large sample techniques for statistics / / Jiming Jiang |
| Autore | Jiang Jiming |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (689 pages) |
| Disciplina | 519.52 |
| Collana | Springer Texts in Statistics |
| Soggetto topico |
Mathematical statistics
Sampling (Statistics) Mostreig (Estadística) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030916954
9783030916947 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 The ε-δ Arguments -- 1.1 Introduction -- 1.2 Getting used to the ε-δ arguments -- 1.3 More examples -- 1.4 Case study: Consistency of MLE in the i.i.d. case -- 1.5 Some useful results -- 1.5.1 Infinite sequence -- 1.5.2 Infinite series -- 1.5.3 Topology -- 1.5.4 Continuity, differentiation, and integration -- 1.6 Exercises -- 2 Modes of Convergence -- 2.1 Introduction -- 2.2 Convergence in probability -- 2.3 Almost sure convergence -- 2.4 Convergence in distribution -- 2.5 Lp convergence and related topics -- 2.6 Case study: χ2-test -- 2.7 Summary and additional results -- 2.8 Exercises -- 3 Big O, Small o, and the Unspecified c -- 3.1 Introduction -- 3.2 Big O and small o for sequences and functions -- 3.3 Big O and small o for vectors and matrices -- 3.4 Big O and small o for random quantities -- 3.5 The unspecified c and other similar methods -- 3.6 Case study: The baseball problem -- 3.7 Case study: Likelihood ratio for a clustering problem -- 3.8 Exercises -- 4 Asymptotic Expansions -- 4.1 Introduction -- 4.2 Taylor expansion -- 4.3 Edgeworth expansion -- method of formal derivation -- 4.4 Other related expansions -- 4.4.1 Fourier series expansion -- 4.4.2 Cornish-Fisher expansion -- 4.4.3 Two time series expansions -- 4.5 Some elementary expansions -- 4.6 Laplace approximation -- 4.7 Case study: Asymptotic distribution of the MLE -- 4.8 Case study: The Prasad-Rao method -- 4.9 Exercises -- 5 Inequalities -- 5.1 Introduction -- 5.2 Numerical inequalities -- 5.2.1 The convex function inequality -- 5.2.2 Hölder's and related inequalities -- 5.2.3 Monotone functions and related inequalities -- 5.3 Matrix inequalities -- 5.3.1 Nonnegative definite matrices -- 5.3.2 Characteristics of matrices -- 5.4 Integral/moment inequalities -- 5.5 Probability inequalities.
5.6 Case study: Some problems on existence of moments -- 5.7 Case study: A variance inequality -- 5.8 Exercises -- 6 Sums of Independent Random Variables -- 6.1 Introduction -- 6.2 The weak law of large numbers -- 6.3 The strong law of large numbers -- 6.4 The central limit theorem -- 6.5 The law of the iterated logarithm -- 6.6 Further results -- 6.6.1 Invariance principles in CLT and LIL -- 6.6.2 Large deviations -- 6.7 Case study: The least squares estimators -- 6.8 Exercises -- 7 Empirical Processes -- 7.1 Introduction -- 7.2 Glivenko-Cantelli theorem and statistical functionals -- 7.3 Weak convergence of empirical processes -- 7.4 LIL and strong approximation -- 7.5 Bounds and large deviations -- 7.6 Non-i.i.d. observations -- 7.7 Empirical processes indexed by functions -- 7.8 Case study: Estimation of ROC curve and ODC -- 7.9 Exercises -- 8 Martingales -- 8.1 Introduction -- 8.2 Examples and simple properties -- 8.3 Two important theorems of martingales -- 8.3.1 The optional stopping theorem -- 8.3.2 The martingale convergence theorem -- 8.4 Martingale laws of large numbers -- 8.4.1 A weak law of large numbers -- 8.4.2 Some strong laws of large numbers -- 8.5 A martingale central limit theorem and related topic -- 8.6 Convergence rate in SLLN and LIL -- 8.7 Invariance principles for martingales -- 8.8 Case study: CLTs for quadratic forms -- 8.9 Case study: Martingale approximation -- 8.10 Exercises -- 9 Time and Spatial Series -- 9.1 Introduction -- 9.2 Autocovariances and autocorrelations -- 9.3 The information criteria -- 9.4 ARMA model identification -- 9.5 Strong limit theorems for i.i.d. spatial series -- 9.6 Two-parameter martingale differences -- 9.7 Sample ACV and ACR for spatial series -- 9.8 Case study: Spatial AR models -- 9.9 Exercises -- 10 Stochastic Processes -- 10.1 Introduction -- 10.2 Markov chains -- 10.3 Poisson processes. 10.4 Renewal theory -- 10.5 Brownian motion -- 10.6 Stochastic integrals and diffusions -- 10.7 Case study: GARCH models and financial SDE -- 10.8 Exercises -- 11 Nonparametric Statistics -- 11.1 Introduction -- 11.2 Some classical nonparametric tests -- 11.3 Asymptotic relative efficiency -- 11.4 Goodness-of-fit tests -- 11.5 U-statistics -- 11.6 Density estimation -- 11.7 Exercises -- 12 Mixed Effects Models -- 12.1 Introduction -- 12.2 REML: Restricted maximum likelihood -- 12.3 Linear mixed model diagnostics -- 12.4 Inference about GLMM -- 12.5 Mixed model selection -- 12.6 Exercises -- 13 Small-Area Estimation -- 13.1 Introduction -- 13.2 Empirical best prediction with binary data -- 13.3 The Fay-Herriot model -- 13.4 Nonparametric small-area estimation -- 13.5 Model selection for small-area estimation -- 13.6 Exercises -- 14 Jackknife and Bootstrap -- 14.1 Introduction -- 14.2 The jackknife -- 14.3 Jackknifing the MSPE of EBP -- 14.4 The bootstrap -- 14.5 Bootstrapping time series -- 14.6 Bootstrapping mixed models -- 14.7 Exercises -- 15 Markov-Chain Monte Carlo -- 15.1 Introduction -- 15.2 The Gibbs sampler -- 15.3 The Metropolis-Hastings algorithm -- 15.4 Monte Carlo EM algorithm -- 15.5 Convergence rates of Gibbs samplers -- 15.6 Exercises -- 16 Random Matrix Theory -- 16.1 Introduction -- 16.2 Fundamental theorems of RMT -- 16.3 Large covariance matrices -- 16.4 High-dimensional linear models -- 16.5 Genome-wide association study -- 16.6 Application to time series -- 16.7 Exercises -- Appendix A -- A.1 Matrix algebra -- A.1.1 Numbers associated with a matrix -- A.1.2 Inverse of a matrix -- A.1.3 Kronecker products -- A.1.4 Matrix differentiation -- A.1.5 Projection -- A.1.6 Decompositions of matrices and eigenvalues -- A.2 Measure and probability -- A.2.1 Measures -- A.2.2 Measurable functions -- A.2.3 Integration. A.2.4 Distributions and random variables -- A.2.5 Conditional expectations -- A.2.6 Conditional distributions -- A.3 Some results in statistics -- A.3.1 The multivariate normal distribution -- A.3.2 Maximum likelihood -- A.3.3 Exponential family and generalized linear models -- A.3.4 Bayesian inference -- A.3.5 Stationary processes -- A.4 List of notation and abbreviations -- References -- Index. |
| Record Nr. | UNISA-996472039303316 |
Jiang Jiming
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Large sample techniques for statistics / / Jiming Jiang
| Large sample techniques for statistics / / Jiming Jiang |
| Autore | Jiang Jiming |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (689 pages) |
| Disciplina | 519.52 |
| Collana | Springer Texts in Statistics |
| Soggetto topico |
Mathematical statistics
Sampling (Statistics) Mostreig (Estadística) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030916954
9783030916947 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 The ε-δ Arguments -- 1.1 Introduction -- 1.2 Getting used to the ε-δ arguments -- 1.3 More examples -- 1.4 Case study: Consistency of MLE in the i.i.d. case -- 1.5 Some useful results -- 1.5.1 Infinite sequence -- 1.5.2 Infinite series -- 1.5.3 Topology -- 1.5.4 Continuity, differentiation, and integration -- 1.6 Exercises -- 2 Modes of Convergence -- 2.1 Introduction -- 2.2 Convergence in probability -- 2.3 Almost sure convergence -- 2.4 Convergence in distribution -- 2.5 Lp convergence and related topics -- 2.6 Case study: χ2-test -- 2.7 Summary and additional results -- 2.8 Exercises -- 3 Big O, Small o, and the Unspecified c -- 3.1 Introduction -- 3.2 Big O and small o for sequences and functions -- 3.3 Big O and small o for vectors and matrices -- 3.4 Big O and small o for random quantities -- 3.5 The unspecified c and other similar methods -- 3.6 Case study: The baseball problem -- 3.7 Case study: Likelihood ratio for a clustering problem -- 3.8 Exercises -- 4 Asymptotic Expansions -- 4.1 Introduction -- 4.2 Taylor expansion -- 4.3 Edgeworth expansion -- method of formal derivation -- 4.4 Other related expansions -- 4.4.1 Fourier series expansion -- 4.4.2 Cornish-Fisher expansion -- 4.4.3 Two time series expansions -- 4.5 Some elementary expansions -- 4.6 Laplace approximation -- 4.7 Case study: Asymptotic distribution of the MLE -- 4.8 Case study: The Prasad-Rao method -- 4.9 Exercises -- 5 Inequalities -- 5.1 Introduction -- 5.2 Numerical inequalities -- 5.2.1 The convex function inequality -- 5.2.2 Hölder's and related inequalities -- 5.2.3 Monotone functions and related inequalities -- 5.3 Matrix inequalities -- 5.3.1 Nonnegative definite matrices -- 5.3.2 Characteristics of matrices -- 5.4 Integral/moment inequalities -- 5.5 Probability inequalities.
5.6 Case study: Some problems on existence of moments -- 5.7 Case study: A variance inequality -- 5.8 Exercises -- 6 Sums of Independent Random Variables -- 6.1 Introduction -- 6.2 The weak law of large numbers -- 6.3 The strong law of large numbers -- 6.4 The central limit theorem -- 6.5 The law of the iterated logarithm -- 6.6 Further results -- 6.6.1 Invariance principles in CLT and LIL -- 6.6.2 Large deviations -- 6.7 Case study: The least squares estimators -- 6.8 Exercises -- 7 Empirical Processes -- 7.1 Introduction -- 7.2 Glivenko-Cantelli theorem and statistical functionals -- 7.3 Weak convergence of empirical processes -- 7.4 LIL and strong approximation -- 7.5 Bounds and large deviations -- 7.6 Non-i.i.d. observations -- 7.7 Empirical processes indexed by functions -- 7.8 Case study: Estimation of ROC curve and ODC -- 7.9 Exercises -- 8 Martingales -- 8.1 Introduction -- 8.2 Examples and simple properties -- 8.3 Two important theorems of martingales -- 8.3.1 The optional stopping theorem -- 8.3.2 The martingale convergence theorem -- 8.4 Martingale laws of large numbers -- 8.4.1 A weak law of large numbers -- 8.4.2 Some strong laws of large numbers -- 8.5 A martingale central limit theorem and related topic -- 8.6 Convergence rate in SLLN and LIL -- 8.7 Invariance principles for martingales -- 8.8 Case study: CLTs for quadratic forms -- 8.9 Case study: Martingale approximation -- 8.10 Exercises -- 9 Time and Spatial Series -- 9.1 Introduction -- 9.2 Autocovariances and autocorrelations -- 9.3 The information criteria -- 9.4 ARMA model identification -- 9.5 Strong limit theorems for i.i.d. spatial series -- 9.6 Two-parameter martingale differences -- 9.7 Sample ACV and ACR for spatial series -- 9.8 Case study: Spatial AR models -- 9.9 Exercises -- 10 Stochastic Processes -- 10.1 Introduction -- 10.2 Markov chains -- 10.3 Poisson processes. 10.4 Renewal theory -- 10.5 Brownian motion -- 10.6 Stochastic integrals and diffusions -- 10.7 Case study: GARCH models and financial SDE -- 10.8 Exercises -- 11 Nonparametric Statistics -- 11.1 Introduction -- 11.2 Some classical nonparametric tests -- 11.3 Asymptotic relative efficiency -- 11.4 Goodness-of-fit tests -- 11.5 U-statistics -- 11.6 Density estimation -- 11.7 Exercises -- 12 Mixed Effects Models -- 12.1 Introduction -- 12.2 REML: Restricted maximum likelihood -- 12.3 Linear mixed model diagnostics -- 12.4 Inference about GLMM -- 12.5 Mixed model selection -- 12.6 Exercises -- 13 Small-Area Estimation -- 13.1 Introduction -- 13.2 Empirical best prediction with binary data -- 13.3 The Fay-Herriot model -- 13.4 Nonparametric small-area estimation -- 13.5 Model selection for small-area estimation -- 13.6 Exercises -- 14 Jackknife and Bootstrap -- 14.1 Introduction -- 14.2 The jackknife -- 14.3 Jackknifing the MSPE of EBP -- 14.4 The bootstrap -- 14.5 Bootstrapping time series -- 14.6 Bootstrapping mixed models -- 14.7 Exercises -- 15 Markov-Chain Monte Carlo -- 15.1 Introduction -- 15.2 The Gibbs sampler -- 15.3 The Metropolis-Hastings algorithm -- 15.4 Monte Carlo EM algorithm -- 15.5 Convergence rates of Gibbs samplers -- 15.6 Exercises -- 16 Random Matrix Theory -- 16.1 Introduction -- 16.2 Fundamental theorems of RMT -- 16.3 Large covariance matrices -- 16.4 High-dimensional linear models -- 16.5 Genome-wide association study -- 16.6 Application to time series -- 16.7 Exercises -- Appendix A -- A.1 Matrix algebra -- A.1.1 Numbers associated with a matrix -- A.1.2 Inverse of a matrix -- A.1.3 Kronecker products -- A.1.4 Matrix differentiation -- A.1.5 Projection -- A.1.6 Decompositions of matrices and eigenvalues -- A.2 Measure and probability -- A.2.1 Measures -- A.2.2 Measurable functions -- A.2.3 Integration. A.2.4 Distributions and random variables -- A.2.5 Conditional expectations -- A.2.6 Conditional distributions -- A.3 Some results in statistics -- A.3.1 The multivariate normal distribution -- A.3.2 Maximum likelihood -- A.3.3 Exponential family and generalized linear models -- A.3.4 Bayesian inference -- A.3.5 Stationary processes -- A.4 List of notation and abbreviations -- References -- Index. |
| Record Nr. | UNINA-9910559398903321 |
|
Jiang Jiming
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Linear and generalized linear mixed models and their applications / / Jiming Jiang and Thuan Nguyen
| Linear and generalized linear mixed models and their applications / / Jiming Jiang and Thuan Nguyen |
| Autore | Jiang Jiming |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New York, New York ; ; London, England : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (352 pages) : illustrations |
| Disciplina | 519.5 |
| Collana | Springer Series in Statistics |
| Soggetto topico |
Mathematical statistics
Linear models (Statistics) Estadística matemàtica Models lineals (Estadística) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 1-0716-1282-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Notations -- 1 Linear Mixed Models: Part I -- 1.1 Introduction -- 1.1.1 Effect of Air Pollution Episodes on Children -- 1.1.2 Genome-Wide Association Study -- 1.1.3 Small Area Estimation of Income -- 1.2 Types of Linear Mixed Models -- 1.2.1 Gaussian Mixed Models -- 1.2.1.1 Mixed ANOVA Model -- 1.2.1.2 Longitudinal Model -- 1.2.1.3 Marginal Model -- 1.2.1.4 Hierarchical Models -- 1.2.2 Non-Gaussian Linear Mixed Models -- 1.2.2.1 Mixed ANOVA Model -- 1.2.2.2 Longitudinal Model -- 1.2.2.3 Marginal Model -- 1.3 Estimation in Gaussian Mixed Models -- 1.3.1 Maximum Likelihood -- 1.3.1.1 Point Estimation -- 1.3.1.2 Asymptotic Covariance Matrix -- 1.3.2 Restricted Maximum Likelihood (REML) -- 1.3.2.1 Point Estimation -- 1.3.2.2 Historical Note -- 1.3.2.3 Asymptotic Covariance Matrix -- 1.4 Estimation in Non-Gaussian Linear Mixed Models -- 1.4.1 Quasi-Likelihood Method -- 1.4.2 Partially Observed Information -- 1.4.3 Iterative Weighted Least Squares -- 1.4.3.1 Balanced Case -- 1.4.3.2 Unbalanced Case -- 1.4.4 Jackknife Method -- 1.4.5 High-Dimensional Misspecified Mixed Model Analysis -- 1.5 Other Methods of Estimation -- 1.5.1 Analysis of Variance Estimation -- 1.5.1.1 Balanced Data -- 1.5.1.2 Unbalanced Data -- 1.5.2 Minimum Norm Quadratic Unbiased Estimation -- 1.6 Notes on Computation and Software -- 1.6.1 Notes on Computation -- 1.6.1.1 Computation of the ML and REML Estimators -- 1.6.1.2 The EM Algorithm -- 1.6.2 Notes on Software -- 1.7 Real-Life Data Examples -- 1.7.1 Analysis of Birth Weights of Lambs -- 1.7.2 Analysis of Hip Replacements Data -- 1.7.3 Analyses of High-Dimensional GWAS Data -- 1.8 Further Results and Technical Notes -- 1.8.1 A Note on Finding the MLE -- 1.8.2 Note on Matrix X Not Being Full Rank -- 1.8.3 Asymptotic Behavior of ML and REML Estimators in Non-Gaussian Mixed ANOVA Models.
1.8.4 Truncated Estimator -- 1.8.5 POQUIM in General -- 1.9 Exercises -- 2 Linear Mixed Models: Part II -- 2.1 Tests in Linear Mixed Models -- 2.1.1 Tests in Gaussian Mixed Models -- 2.1.1.1 Exact Tests -- 2.1.1.2 Optimal Tests -- 2.1.1.3 Likelihood-Ratio Tests -- 2.1.2 Tests in Non-Gaussian Linear Mixed Models -- 2.1.2.1 Empirical Method of Moments -- 2.1.2.2 Partially Observed Information -- 2.1.2.3 Jackknife Method -- 2.1.2.4 Robust Versions of Classical Tests -- 2.2 Confidence Intervals in Linear Mixed Models -- 2.2.1 Confidence Intervals in Gaussian Mixed Models -- 2.2.1.1 Exact Confidence Intervals for Variance Components -- 2.2.1.2 Approximate Confidence Intervals for Variance Components -- 2.2.1.3 Simultaneous Confidence Intervals -- 2.2.1.4 Confidence Intervals for Fixed Effects -- 2.2.2 Confidence Intervals in Non-Gaussian Linear MixedModels -- 2.2.2.1 ANOVA Models -- 2.2.2.2 Longitudinal Models -- 2.3 Prediction -- 2.3.1 Best Prediction -- 2.3.2 Best Linear Unbiased Prediction -- 2.3.2.1 Empirical BLUP -- 2.3.3 Observed Best Prediction -- 2.3.4 Prediction of Future Observation -- 2.3.4.1 Distribution-Free Prediction Intervals -- 2.3.4.2 Standard Linear Mixed Models -- 2.3.4.3 Nonstandard Linear Mixed Models -- 2.3.4.4 A Simulated Example -- 2.3.5 Classified Mixed Model Prediction -- 2.3.5.1 CMMP of Mixed Effects -- 2.3.5.2 CMMP of Future Observation -- 2.3.5.3 CMMP When the Actual Match Does Not Exist -- 2.3.5.4 Empirical Demonstration -- 2.3.5.5 Incorporating Covariate Information in Matching -- 2.3.5.6 More Empirical Demonstration -- 2.3.5.7 Prediction Interval -- 2.4 Model Checking and Selection -- 2.4.1 Model Diagnostics -- 2.4.1.1 Diagnostic Plots -- 2.4.1.2 Goodness-of-Fit Tests -- 2.4.2 Information Criteria -- 2.4.2.1 Selection with Fixed Random Factors -- 2.4.2.2 Selection with Random Factors -- 2.4.3 The Fence Methods. 2.4.3.1 The Effective Sample Size -- 2.4.3.2 The Dimension of a Model -- 2.4.3.3 Unknown Distribution -- 2.4.3.4 Finite-Sample Performance and the Effect of a Constant -- 2.4.3.5 Criterion of Optimality -- 2.4.4 Shrinkage Mixed Model Selection -- 2.5 Bayesian Inference -- 2.5.1 Inference About Variance Components -- 2.5.2 Inference About Fixed and Random Effects -- 2.6 Real-Life Data Examples -- 2.6.1 Reliability of Environmental Sampling -- 2.6.2 Hospital Data -- 2.6.3 Baseball Example -- 2.6.4 Iowa Crops Data -- 2.6.5 Analysis of High-Speed Network Data -- 2.7 Further Results and Technical Notes -- 2.7.1 Robust Versions of Classical Tests -- 2.7.2 Existence of Moments of ML/REML Estimators -- 2.7.3 Existence of Moments of EBLUE and EBLUP -- 2.7.4 The Definition of Σn(θ) in Sect.2.4.1.2 -- 2.8 Exercises -- 3 Generalized Linear Mixed Models: Part I -- 3.1 Introduction -- 3.2 Generalized Linear Mixed Models -- 3.3 Real-Life Data Examples -- 3.3.1 Salamander Mating Experiments -- 3.3.2 A Log-Linear Mixed Model for Seizure Counts -- 3.3.3 Small Area Estimation of Mammography Rates -- 3.4 Likelihood Function Under GLMM -- 3.5 Approximate Inference -- 3.5.1 Laplace Approximation -- 3.5.2 Penalized Quasi-likelihood Estimation -- 3.5.2.1 Derivation of PQL -- 3.5.2.2 Computational Procedures -- 3.5.2.3 Variance Components -- 3.5.2.4 Inconsistency of PQL Estimators -- 3.5.3 Tests of Zero Variance Components -- 3.5.4 Maximum Hierarchical Likelihood -- 3.5.5 Note on Existing Software -- 3.6 GLMM Prediction -- 3.6.1 Joint Estimation of Fixed and Random Effects -- 3.6.1.1 Maximum a Posterior -- 3.6.1.2 Computation of MPE -- 3.6.1.3 Penalized Generalized WLS -- 3.6.1.4 Maximum Conditional Likelihood -- 3.6.1.5 Quadratic Inference Function -- 3.6.2 Empirical Best Prediction -- 3.6.2.1 Empirical Best Prediction Under GLMM -- 3.6.2.2 Model-Assisted EBP. 3.6.3 A Simulated Example -- 3.6.4 Classified Mixed Logistic Model Prediction -- 3.6.5 Best Look-Alike Prediction -- 3.6.5.1 BLAP of a Discrete/Categorical Random Variable -- 3.6.5.2 BLAP of a Zero-Inflated Random Variable -- 3.7 Real-Life Data Example Follow-Ups and More -- 3.7.1 Salamander Mating Data -- 3.7.2 Seizure Count Data -- 3.7.3 Mammography Rates -- 3.7.4 Analysis of ECMO Data -- 3.7.4.1 Prediction of Mixed Effects of Interest -- 3.8 Further Results and Technical Notes -- 3.8.1 More on NLGSA -- 3.8.2 Asymptotic Properties of PQWLS Estimators -- 3.8.3 MSPE of EBP -- 3.8.4 MSPE of the Model-Assisted EBP -- 3.9 Exercises -- 4 Generalized Linear Mixed Models: Part II -- 4.1 Likelihood-Based Inference -- 4.1.1 A Monte Carlo EM Algorithm for Binary Data -- 4.1.1.1 The EM Algorithm -- 4.1.1.2 Monte Carlo EM via Gibbs Sampler -- 4.1.2 Extensions -- 4.1.2.1 MCEM with Metropolis-Hastings Algorithm -- 4.1.2.2 Monte Carlo Newton-Raphson Procedure -- 4.1.2.3 Simulated ML -- 4.1.3 MCEM with i.i.d. Sampling -- 4.1.3.1 Importance Sampling -- 4.1.3.2 Rejection Sampling -- 4.1.4 Automation -- 4.1.5 Data Cloning -- 4.1.6 Maximization by Parts -- 4.1.7 Bayesian Inference -- 4.2 Estimating Equations -- 4.2.1 Generalized Estimating Equations (GEE) -- 4.2.2 Iterative Estimating Equations -- 4.2.3 Method of Simulated Moments -- 4.2.4 Robust Estimation in GLMM -- 4.3 GLMM Diagnostics and Selection -- 4.3.1 A Goodness-of-Fit Test for GLMM Diagnostics -- 4.3.1.1 Tailoring -- 4.3.1.2 χ2-Test -- 4.3.1.3 Application to GLMM -- 4.3.2 Fence Methods for GLMM Selection -- 4.3.2.1 Maximum Likelihood (ML) Model Selection -- 4.3.2.2 Mean and Variance/Covariance (MVC) Model Selection -- 4.3.2.3 Extended GLMM Selection -- 4.3.3 Two Examples with Simulation -- 4.3.3.1 A Simulated Example of GLMM Diagnostics -- 4.3.3.2 A Simulated Example of GLMM Selection. 4.4 Real-Life Data Examples -- 4.4.1 Fetal Mortality in Mouse Litters -- 4.4.2 Analysis of Gc Genotype Data -- 4.4.3 Salamander Mating Experiments Revisited -- 4.4.4 The National Health Interview Survey -- 4.5 Further Results and Technical Notes -- 4.5.1 Proof of Theorem 4.3 -- 4.5.2 Linear Convergence and Asymptotic Properties of IEE -- 4.5.2.1 Linear Convergence -- 4.5.2.2 Asymptotic Behavior of IEEE -- 4.5.3 Incorporating Informative Missing Data in IEE -- 4.5.4 Consistency of MSM Estimator -- 4.5.5 Asymptotic Properties of First- and Second-StepEstimators -- 4.5.6 Further Details Regarding the Fence Methods -- 4.5.6.1 Estimation of σM,M* in Case of Clustered Observations -- 4.5.6.2 Consistency of the Fence -- 4.5.7 Consistency of MLE in GLMM with Crossed Random Effects -- 4.6 Exercises -- A Matrix Algebra -- A.1 Kronecker Products -- A.2 Matrix Differentiation -- A.3 Projection and Related Results -- A.4 Inverse and Generalized Inverse -- A.5 Decompositions of Matrices -- A.6 The Eigenvalue Perturbation Theory -- B Some Results in Statistics -- B.1 Multivariate Normal Distribution -- B.2 Quadratic Forms -- B.3 OP and oP -- B.4 Convolution -- B.5 Exponential Family and Generalized Linear Models -- References -- Index. |
| Record Nr. | UNISA-996466561103316 |
|
Jiang Jiming
|
||
| New York, New York ; ; London, England : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Linear and generalized linear mixed models and their applications / / Jiming Jiang and Thuan Nguyen
| Linear and generalized linear mixed models and their applications / / Jiming Jiang and Thuan Nguyen |
| Autore | Jiang Jiming |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New York, New York ; ; London, England : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (352 pages) : illustrations |
| Disciplina | 519.5 |
| Collana | Springer Series in Statistics |
| Soggetto topico |
Mathematical statistics
Linear models (Statistics) Estadística matemàtica Models lineals (Estadística) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 1-0716-1282-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Notations -- 1 Linear Mixed Models: Part I -- 1.1 Introduction -- 1.1.1 Effect of Air Pollution Episodes on Children -- 1.1.2 Genome-Wide Association Study -- 1.1.3 Small Area Estimation of Income -- 1.2 Types of Linear Mixed Models -- 1.2.1 Gaussian Mixed Models -- 1.2.1.1 Mixed ANOVA Model -- 1.2.1.2 Longitudinal Model -- 1.2.1.3 Marginal Model -- 1.2.1.4 Hierarchical Models -- 1.2.2 Non-Gaussian Linear Mixed Models -- 1.2.2.1 Mixed ANOVA Model -- 1.2.2.2 Longitudinal Model -- 1.2.2.3 Marginal Model -- 1.3 Estimation in Gaussian Mixed Models -- 1.3.1 Maximum Likelihood -- 1.3.1.1 Point Estimation -- 1.3.1.2 Asymptotic Covariance Matrix -- 1.3.2 Restricted Maximum Likelihood (REML) -- 1.3.2.1 Point Estimation -- 1.3.2.2 Historical Note -- 1.3.2.3 Asymptotic Covariance Matrix -- 1.4 Estimation in Non-Gaussian Linear Mixed Models -- 1.4.1 Quasi-Likelihood Method -- 1.4.2 Partially Observed Information -- 1.4.3 Iterative Weighted Least Squares -- 1.4.3.1 Balanced Case -- 1.4.3.2 Unbalanced Case -- 1.4.4 Jackknife Method -- 1.4.5 High-Dimensional Misspecified Mixed Model Analysis -- 1.5 Other Methods of Estimation -- 1.5.1 Analysis of Variance Estimation -- 1.5.1.1 Balanced Data -- 1.5.1.2 Unbalanced Data -- 1.5.2 Minimum Norm Quadratic Unbiased Estimation -- 1.6 Notes on Computation and Software -- 1.6.1 Notes on Computation -- 1.6.1.1 Computation of the ML and REML Estimators -- 1.6.1.2 The EM Algorithm -- 1.6.2 Notes on Software -- 1.7 Real-Life Data Examples -- 1.7.1 Analysis of Birth Weights of Lambs -- 1.7.2 Analysis of Hip Replacements Data -- 1.7.3 Analyses of High-Dimensional GWAS Data -- 1.8 Further Results and Technical Notes -- 1.8.1 A Note on Finding the MLE -- 1.8.2 Note on Matrix X Not Being Full Rank -- 1.8.3 Asymptotic Behavior of ML and REML Estimators in Non-Gaussian Mixed ANOVA Models.
1.8.4 Truncated Estimator -- 1.8.5 POQUIM in General -- 1.9 Exercises -- 2 Linear Mixed Models: Part II -- 2.1 Tests in Linear Mixed Models -- 2.1.1 Tests in Gaussian Mixed Models -- 2.1.1.1 Exact Tests -- 2.1.1.2 Optimal Tests -- 2.1.1.3 Likelihood-Ratio Tests -- 2.1.2 Tests in Non-Gaussian Linear Mixed Models -- 2.1.2.1 Empirical Method of Moments -- 2.1.2.2 Partially Observed Information -- 2.1.2.3 Jackknife Method -- 2.1.2.4 Robust Versions of Classical Tests -- 2.2 Confidence Intervals in Linear Mixed Models -- 2.2.1 Confidence Intervals in Gaussian Mixed Models -- 2.2.1.1 Exact Confidence Intervals for Variance Components -- 2.2.1.2 Approximate Confidence Intervals for Variance Components -- 2.2.1.3 Simultaneous Confidence Intervals -- 2.2.1.4 Confidence Intervals for Fixed Effects -- 2.2.2 Confidence Intervals in Non-Gaussian Linear MixedModels -- 2.2.2.1 ANOVA Models -- 2.2.2.2 Longitudinal Models -- 2.3 Prediction -- 2.3.1 Best Prediction -- 2.3.2 Best Linear Unbiased Prediction -- 2.3.2.1 Empirical BLUP -- 2.3.3 Observed Best Prediction -- 2.3.4 Prediction of Future Observation -- 2.3.4.1 Distribution-Free Prediction Intervals -- 2.3.4.2 Standard Linear Mixed Models -- 2.3.4.3 Nonstandard Linear Mixed Models -- 2.3.4.4 A Simulated Example -- 2.3.5 Classified Mixed Model Prediction -- 2.3.5.1 CMMP of Mixed Effects -- 2.3.5.2 CMMP of Future Observation -- 2.3.5.3 CMMP When the Actual Match Does Not Exist -- 2.3.5.4 Empirical Demonstration -- 2.3.5.5 Incorporating Covariate Information in Matching -- 2.3.5.6 More Empirical Demonstration -- 2.3.5.7 Prediction Interval -- 2.4 Model Checking and Selection -- 2.4.1 Model Diagnostics -- 2.4.1.1 Diagnostic Plots -- 2.4.1.2 Goodness-of-Fit Tests -- 2.4.2 Information Criteria -- 2.4.2.1 Selection with Fixed Random Factors -- 2.4.2.2 Selection with Random Factors -- 2.4.3 The Fence Methods. 2.4.3.1 The Effective Sample Size -- 2.4.3.2 The Dimension of a Model -- 2.4.3.3 Unknown Distribution -- 2.4.3.4 Finite-Sample Performance and the Effect of a Constant -- 2.4.3.5 Criterion of Optimality -- 2.4.4 Shrinkage Mixed Model Selection -- 2.5 Bayesian Inference -- 2.5.1 Inference About Variance Components -- 2.5.2 Inference About Fixed and Random Effects -- 2.6 Real-Life Data Examples -- 2.6.1 Reliability of Environmental Sampling -- 2.6.2 Hospital Data -- 2.6.3 Baseball Example -- 2.6.4 Iowa Crops Data -- 2.6.5 Analysis of High-Speed Network Data -- 2.7 Further Results and Technical Notes -- 2.7.1 Robust Versions of Classical Tests -- 2.7.2 Existence of Moments of ML/REML Estimators -- 2.7.3 Existence of Moments of EBLUE and EBLUP -- 2.7.4 The Definition of Σn(θ) in Sect.2.4.1.2 -- 2.8 Exercises -- 3 Generalized Linear Mixed Models: Part I -- 3.1 Introduction -- 3.2 Generalized Linear Mixed Models -- 3.3 Real-Life Data Examples -- 3.3.1 Salamander Mating Experiments -- 3.3.2 A Log-Linear Mixed Model for Seizure Counts -- 3.3.3 Small Area Estimation of Mammography Rates -- 3.4 Likelihood Function Under GLMM -- 3.5 Approximate Inference -- 3.5.1 Laplace Approximation -- 3.5.2 Penalized Quasi-likelihood Estimation -- 3.5.2.1 Derivation of PQL -- 3.5.2.2 Computational Procedures -- 3.5.2.3 Variance Components -- 3.5.2.4 Inconsistency of PQL Estimators -- 3.5.3 Tests of Zero Variance Components -- 3.5.4 Maximum Hierarchical Likelihood -- 3.5.5 Note on Existing Software -- 3.6 GLMM Prediction -- 3.6.1 Joint Estimation of Fixed and Random Effects -- 3.6.1.1 Maximum a Posterior -- 3.6.1.2 Computation of MPE -- 3.6.1.3 Penalized Generalized WLS -- 3.6.1.4 Maximum Conditional Likelihood -- 3.6.1.5 Quadratic Inference Function -- 3.6.2 Empirical Best Prediction -- 3.6.2.1 Empirical Best Prediction Under GLMM -- 3.6.2.2 Model-Assisted EBP. 3.6.3 A Simulated Example -- 3.6.4 Classified Mixed Logistic Model Prediction -- 3.6.5 Best Look-Alike Prediction -- 3.6.5.1 BLAP of a Discrete/Categorical Random Variable -- 3.6.5.2 BLAP of a Zero-Inflated Random Variable -- 3.7 Real-Life Data Example Follow-Ups and More -- 3.7.1 Salamander Mating Data -- 3.7.2 Seizure Count Data -- 3.7.3 Mammography Rates -- 3.7.4 Analysis of ECMO Data -- 3.7.4.1 Prediction of Mixed Effects of Interest -- 3.8 Further Results and Technical Notes -- 3.8.1 More on NLGSA -- 3.8.2 Asymptotic Properties of PQWLS Estimators -- 3.8.3 MSPE of EBP -- 3.8.4 MSPE of the Model-Assisted EBP -- 3.9 Exercises -- 4 Generalized Linear Mixed Models: Part II -- 4.1 Likelihood-Based Inference -- 4.1.1 A Monte Carlo EM Algorithm for Binary Data -- 4.1.1.1 The EM Algorithm -- 4.1.1.2 Monte Carlo EM via Gibbs Sampler -- 4.1.2 Extensions -- 4.1.2.1 MCEM with Metropolis-Hastings Algorithm -- 4.1.2.2 Monte Carlo Newton-Raphson Procedure -- 4.1.2.3 Simulated ML -- 4.1.3 MCEM with i.i.d. Sampling -- 4.1.3.1 Importance Sampling -- 4.1.3.2 Rejection Sampling -- 4.1.4 Automation -- 4.1.5 Data Cloning -- 4.1.6 Maximization by Parts -- 4.1.7 Bayesian Inference -- 4.2 Estimating Equations -- 4.2.1 Generalized Estimating Equations (GEE) -- 4.2.2 Iterative Estimating Equations -- 4.2.3 Method of Simulated Moments -- 4.2.4 Robust Estimation in GLMM -- 4.3 GLMM Diagnostics and Selection -- 4.3.1 A Goodness-of-Fit Test for GLMM Diagnostics -- 4.3.1.1 Tailoring -- 4.3.1.2 χ2-Test -- 4.3.1.3 Application to GLMM -- 4.3.2 Fence Methods for GLMM Selection -- 4.3.2.1 Maximum Likelihood (ML) Model Selection -- 4.3.2.2 Mean and Variance/Covariance (MVC) Model Selection -- 4.3.2.3 Extended GLMM Selection -- 4.3.3 Two Examples with Simulation -- 4.3.3.1 A Simulated Example of GLMM Diagnostics -- 4.3.3.2 A Simulated Example of GLMM Selection. 4.4 Real-Life Data Examples -- 4.4.1 Fetal Mortality in Mouse Litters -- 4.4.2 Analysis of Gc Genotype Data -- 4.4.3 Salamander Mating Experiments Revisited -- 4.4.4 The National Health Interview Survey -- 4.5 Further Results and Technical Notes -- 4.5.1 Proof of Theorem 4.3 -- 4.5.2 Linear Convergence and Asymptotic Properties of IEE -- 4.5.2.1 Linear Convergence -- 4.5.2.2 Asymptotic Behavior of IEEE -- 4.5.3 Incorporating Informative Missing Data in IEE -- 4.5.4 Consistency of MSM Estimator -- 4.5.5 Asymptotic Properties of First- and Second-StepEstimators -- 4.5.6 Further Details Regarding the Fence Methods -- 4.5.6.1 Estimation of σM,M* in Case of Clustered Observations -- 4.5.6.2 Consistency of the Fence -- 4.5.7 Consistency of MLE in GLMM with Crossed Random Effects -- 4.6 Exercises -- A Matrix Algebra -- A.1 Kronecker Products -- A.2 Matrix Differentiation -- A.3 Projection and Related Results -- A.4 Inverse and Generalized Inverse -- A.5 Decompositions of Matrices -- A.6 The Eigenvalue Perturbation Theory -- B Some Results in Statistics -- B.1 Multivariate Normal Distribution -- B.2 Quadratic Forms -- B.3 OP and oP -- B.4 Convolution -- B.5 Exponential Family and Generalized Linear Models -- References -- Index. |
| Record Nr. | UNINA-9910484963903321 |
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Jiang Jiming
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| New York, New York ; ; London, England : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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