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Examples and problems in mathematical statistics / / Shelemyahu Zacks
| Examples and problems in mathematical statistics / / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (654 p.) |
| Disciplina | 519.5 |
| Collana | Wiley Series in Probability and Statistics. |
| Soggetto topico |
Mathematical statistics
Statistics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-60583-7
1-118-60600-0 |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Examples and Problems in Mathematical Statistics; Contents; Preface; List of Random Variables; List of Abbreviations; 1 Basic Probability Theory; PART I: THEORY; 1.1 OPERATIONS ON SETS; 1.2 ALGEBRA AND σ-FIELDS; 1.3 PROBABILITY SPACES; 1.4 CONDITIONAL PROBABILITIES AND INDEPENDENCE; 1.5 RANDOM VARIABLES AND THEIR DISTRIBUTIONS; 1.6 THE LEBESGUE AND STIELTJES INTEGRALS; 1.6.1 General Definition of Expected Value: The Lebesgue Integral; 1.6.2 The Stieltjes-Riemann Integral; 1.6.3 Mixtures of Discrete and Absolutely Continuous Distributions; 1.6.4 Quantiles of Distributions
1.6.5 Transformations1.7 JOINT DISTRIBUTIONS, CONDITIONAL DISTRIBUTIONS AND INDEPENDENCE; 1.7.1 Joint Distributions; 1.7.2 Conditional Expectations: General Definition; 1.7.3 Independence; 1.8 MOMENTS AND RELATED FUNCTIONALS; 1.9 MODES OF CONVERGENCE; 1.10 WEAK CONVERGENCE; 1.11 LAWS OF LARGE NUMBERS; 1.11.1 The Weak Law of Large Numbers (WLLN); 1.11.2 The Strong Law of Large Numbers (SLLN); 1.12 CENTRAL LIMIT THEOREM; 1.13 MISCELLANEOUS RESULTS; 1.13.1 Law of the Iterated Logarithm; 1.13.2 Uniform Integrability; 1.13.3 Inequalities; 1.13.4 The Delta Method; 1.13.5 The Symbols op and Op 1.13.6 The Empirical Distribution and Sample QuantilesPART II: EXAMPLES; PART III: PROBLEMS; PART IV: SOLUTIONS TO SELECTED PROBLEMS; 2 Statistical Distributions; PART I: THEORY; 2.1 INTRODUCTORY REMARKS; 2.2 FAMILIES OF DISCRETE DISTRIBUTIONS; 2.2.1 Binomial Distributions; 2.2.2 Hypergeometric Distributions; 2.2.3 Poisson Distributions; 2.2.4 Geometric, Pascal, and Negative Binomial Distributions; 2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS; 2.3.1 Rectangular Distributions; 2.3.2 Beta Distributions; 2.3.3 Gamma Distributions; 2.3.4 Weibull and Extreme Value Distributions 2.3.5 Normal Distributions2.3.6 Normal Approximations; 2.4 TRANSFORMATIONS; 2.4.1 One-to-One Transformations of Several Variables; 2.4.2 Distribution of Sums; 2.4.3 Distribution of Ratios; 2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS; 2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS; 2.6.1 The Multinomial Distribution; 2.6.2 Multivariate Negative Binomial; 2.6.3 Multivariate Hypergeometric Distributions; 2.7 MULTINORMAL DISTRIBUTIONS; 2.7.1 Basic Theory; 2.7.2 Distribution of Subvectors and Distributions of Linear Forms; 2.7.3 Independence of Linear Forms 2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES; 2.10 THE ORDER STATISTICS; 2.11 t-DISTRIBUTIONS; 2.12 F-DISTRIBUTIONS; 2.13 THE DISTRIBUTION OF THE SAMPLE CORRELATION; 2.14 EXPONENTIAL TYPE FAMILIES; 2.15 APPROXIMATING THE DISTRIBUTION OF THE SAMPLE MEAN: EDGEWORTH AND SADDLEPOINT APPROXIMATIONS; 2.15.1 Edgeworth Expansion; 2.15.2 Saddlepoint Approximation; PART II: EXAMPLES; PART III: PROBLEMS; PART IV: SOLUTIONS TO SELECTED PROBLEMS; 3 Sufficient Statistics and the Information in Samples; PART I: THEORY 3.1 INTRODUCTION |
| Record Nr. | UNINA-9910453411503321 |
Zacks Shelemyahu <1932->
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Examples and problems in mathematical statistics / / Shelemyahu Zacks
| Examples and problems in mathematical statistics / / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (654 pages) |
| Disciplina | 519.5 |
| Soggetto topico |
Mathematical statistics
Statistics |
| ISBN |
1-118-60583-7
1-118-60600-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795972703321 |
|
Zacks Shelemyahu <1932->
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Examples and problems in mathematical statistics / / Shelemyahu Zacks
| Examples and problems in mathematical statistics / / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (654 pages) |
| Disciplina | 519.5 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Mathematical statistics
Statistics |
| ISBN |
1-118-60583-7
1-118-60600-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Examples and Problems in Mathematical Statistics -- Contents -- Preface -- List of Random Variables -- List of Abbreviations -- 1 Basic Probability Theory -- PART I: THEORY -- 1.1 OPERATIONS ON SETS -- 1.2 ALGEBRA AND σ-FIELDS -- 1.3 PROBABILITY SPACES -- 1.4 CONDITIONAL PROBABILITIES AND INDEPENDENCE -- 1.5 RANDOM VARIABLES AND THEIR DISTRIBUTIONS -- 1.6 THE LEBESGUE AND STIELTJES INTEGRALS -- 1.6.1 General Definition of Expected Value: The Lebesgue Integral -- 1.6.2 The Stieltjes-Riemann Integral -- 1.6.3 Mixtures of Discrete and Absolutely Continuous Distributions -- 1.6.4 Quantiles of Distributions -- 1.6.5 Transformations -- 1.7 JOINT DISTRIBUTIONS, CONDITIONAL DISTRIBUTIONS AND INDEPENDENCE -- 1.7.1 Joint Distributions -- 1.7.2 Conditional Expectations: General Definition -- 1.7.3 Independence -- 1.8 MOMENTS AND RELATED FUNCTIONALS -- 1.9 MODES OF CONVERGENCE -- 1.10 WEAK CONVERGENCE -- 1.11 LAWS OF LARGE NUMBERS -- 1.11.1 The Weak Law of Large Numbers (WLLN) -- 1.11.2 The Strong Law of Large Numbers (SLLN) -- 1.12 CENTRAL LIMIT THEOREM -- 1.13 MISCELLANEOUS RESULTS -- 1.13.1 Law of the Iterated Logarithm -- 1.13.2 Uniform Integrability -- 1.13.3 Inequalities -- 1.13.4 The Delta Method -- 1.13.5 The Symbols op and Op -- 1.13.6 The Empirical Distribution and Sample Quantiles -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS TO SELECTED PROBLEMS -- 2 Statistical Distributions -- PART I: THEORY -- 2.1 INTRODUCTORY REMARKS -- 2.2 FAMILIES OF DISCRETE DISTRIBUTIONS -- 2.2.1 Binomial Distributions -- 2.2.2 Hypergeometric Distributions -- 2.2.3 Poisson Distributions -- 2.2.4 Geometric, Pascal, and Negative Binomial Distributions -- 2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS -- 2.3.1 Rectangular Distributions -- 2.3.2 Beta Distributions -- 2.3.3 Gamma Distributions -- 2.3.4 Weibull and Extreme Value Distributions.
2.3.5 Normal Distributions -- 2.3.6 Normal Approximations -- 2.4 TRANSFORMATIONS -- 2.4.1 One-to-One Transformations of Several Variables -- 2.4.2 Distribution of Sums -- 2.4.3 Distribution of Ratios -- 2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS -- 2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS -- 2.6.1 The Multinomial Distribution -- 2.6.2 Multivariate Negative Binomial -- 2.6.3 Multivariate Hypergeometric Distributions -- 2.7 MULTINORMAL DISTRIBUTIONS -- 2.7.1 Basic Theory -- 2.7.2 Distribution of Subvectors and Distributions of Linear Forms -- 2.7.3 Independence of Linear Forms -- 2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES -- 2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES -- 2.10 THE ORDER STATISTICS -- 2.11 t-DISTRIBUTIONS -- 2.12 F-DISTRIBUTIONS -- 2.13 THE DISTRIBUTION OF THE SAMPLE CORRELATION -- 2.14 EXPONENTIAL TYPE FAMILIES -- 2.15 APPROXIMATING THE DISTRIBUTION OF THE SAMPLE MEAN: EDGEWORTH AND SADDLEPOINT APPROXIMATIONS -- 2.15.1 Edgeworth Expansion -- 2.15.2 Saddlepoint Approximation -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS TO SELECTED PROBLEMS -- 3 Sufficient Statistics and the Information in Samples -- PART I: THEORY -- 3.1 INTRODUCTION -- 3.2 DEFINITION AND CHARACTERIZATION OF SUFFICIENT STATISTICS -- 3.2.1 Introductory Discussion -- 3.2.2 Theoretical Formulation -- 3.3 LIKELIHOOD FUNCTIONS AND MINIMAL SUFFICIENT STATISTICS -- 3.4 SUFFICIENT STATISTICS AND EXPONENTIAL TYPE FAMILIES -- 3.5 SUFFICIENCY AND COMPLETENESS -- 3.6 SUFFICIENCY AND ANCILLARITY -- 3.7 INFORMATION FUNCTIONS AND SUFFICIENCY -- 3.7.1 The Fisher Information -- 3.7.2 The Kullback-Leibler Information -- 3.8 THE FISHER INFORMATION MATRIX -- 3.9 SENSITIVITY TO CHANGES IN PARAMETERS -- 3.9.1 The Hellinger Distance -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS TO SELECTED PROBLEMS. 4 Testing Statistical Hypotheses -- PART I: THEORY -- 4.1 THE GENERAL FRAMEWORK -- 4.2 THE NEYMAN-PEARSON FUNDAMENTAL LEMMA -- 4.3 TESTING ONE-SIDED COMPOSITE HYPOTHESES IN MLR MODELS -- 4.4 TESTING TWO-SIDED HYPOTHESES IN ONE-PARAMETER EXPONENTIAL FAMILIES -- 4.5 TESTING COMPOSITE HYPOTHESES WITH NUISANCE PARAMETERS-UNBIASED TESTS -- 4.6 LIKELIHOOD RATIO TESTS -- 4.6.1 Testing in Normal Regression Theory -- 4.6.2 Comparison of Normal Means: The Analysis of Variance -- 4.7 THE ANALYSIS OF CONTINGENCY TABLES -- 4.7.1 The Structure of Multi-Way Contingency Tables and the Statistical Model -- 4.7.2 Testing the Significance of Association -- 4.7.3 The Analysis of Tables -- 4.7.4 Likelihood Ratio Tests for Categorical Data -- 4.8 SEQUENTIAL TESTING OF HYPOTHESES -- 4.8.1 The Wald Sequential Probability Ratio Test -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS TO SELECTED PROBLEMS -- 5 Statistical Estimation -- PART I: THEORY -- 5.1 GENERAL DISCUSSION -- 5.2 UNBIASED ESTIMATORS -- 5.2.1 General Definition and Example -- 5.2.2 Minimum Variance Unbiased Estimators -- 5.2.3 The Cramér-Rao Lower Bound for the One-Parameter Case -- 5.2.4 Extension of the Cramér-Rao Inequality to Multiparameter Cases -- 5.2.5 General Inequalities of the Cramér-Rao Type -- 5.3 THE EFFICIENCY OF UNBIASED ESTIMATORS IN REGULAR CASES -- 5.4 BEST LINEAR UNBIASED AND LEAST-SQUARES ESTIMATORS -- 5.4.1 BLUEs of the Mean -- 5.4.2 Least-Squares and BLUEs in Linear Models -- 5.4.3 Best Linear Combinations of Order Statistics -- 5.5 STABILIZING THE LSE: RIDGE REGRESSIONS -- 5.6 MAXIMUM LIKELIHOOD ESTIMATORS -- 5.6.1 Definition and Examples -- 5.6.2 MLEs in Exponential Type Families -- 5.6.3 The Invariance Principle -- 5.6.4 MLE of the Parameters of Tolerance Distributions -- 5.7 EQUIVARIANT ESTIMATORS -- 5.7.1 The Structure of Equivariant Estimators. 5.7.2 Minimum MSE Equivariant Estimators -- 5.7.3 Minimum Risk Equivariant Estimators -- 5.7.4 The Pitman Estimators -- 5.8 ESTIMATING EQUATIONS -- 5.8.1 Moment-Equations Estimators -- 5.8.2 General Theory of Estimating Functions -- 5.9 PRETEST ESTIMATORS -- 5.10 ROBUST ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF SYMMETRIC DISTRIBUTIONS -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS OF SELECTED PROBLEMS -- 6 Confidence and Tolerance Intervals -- PART I: THEORY -- 6.1 GENERAL INTRODUCTION -- 6.2 THE CONSTRUCTION OF CONFIDENCE INTERVALS -- 6.3 OPTIMAL CONFIDENCE INTERVALS -- 6.4 TOLERANCE INTERVALS -- 6.5 DISTRIBUTION FREE CONFIDENCE AND TOLERANCE INTERVALS -- 6.6 SIMULTANEOUS CONFIDENCE INTERVALS -- 6.7 TWO-STAGE AND SEQUENTIAL SAMPLING FOR FIXED WIDTH CONFIDENCE INTERVALS -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTION TO SELECTED PROBLEMS -- 7 Large Sample Theory for Estimation and Testing -- PART I: THEORY -- 7.1 CONSISTENCY OF ESTIMATORS AND TESTS -- 7.2 CONSISTENCY OF THE MLE -- 7.3 ASYMPTOTIC NORMALITY AND EFFICIENCY OF CONSISTENT ESTIMATORS -- 7.4 SECOND-ORDER EFFICIENCY OF BAN ESTIMATORS -- 7.5 LARGE SAMPLE CONFIDENCE INTERVALS -- 7.6 EDGEWORTH AND SADDLEPOINT APPROXIMATIONS TO THE DISTRIBUTION OF THE MLE: ONE-PARAMETER CANONICAL EXPONENTIAL FAMILIES -- 7.7 LARGE SAMPLE TESTS -- 7.8 PITMAN'S ASYMPTOTIC EFFICIENCY OF TESTS -- 7.9 ASYMPTOTIC PROPERTIES OF SAMPLE QUANTILES -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTION OF SELECTED PROBLEMS -- 8 Bayesian Analysis in Testing and Estimation -- PART I: THEORY -- 8.1 THE BAYESIAN FRAMEWORK -- 8.1.1 Prior, Posterior, and Predictive Distributions -- 8.1.2 Noninformative and Improper Prior Distributions -- 8.1.3 Risk Functions and Bayes Procedures -- 8.2 BAYESIAN TESTING OF HYPOTHESIS -- 8.2.1 Testing Simple Hypothesis. 8.2.2 Testing Composite Hypotheses -- 8.2.3 Bayes Sequential Testing of Hypotheses -- 8.3 BAYESIAN CREDIBILITY AND PREDICTION INTERVALS -- 8.3.1 Credibility Intervals -- 8.3.2 Prediction Intervals -- 8.4 BAYESIAN ESTIMATION -- 8.4.1 General Discussion and Examples -- 8.4.2 Hierarchical Models -- 8.4.3 The Normal Dynamic Linear Model -- 8.5 APPROXIMATION METHODS -- 8.5.1 Analytical Approximations -- 8.5.2 Numerical Approximations -- 8.6 EMPIRICAL BAYES ESTIMATORS -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS OF SELECTED PROBLEMS -- 9 Advanced Topics in Estimation Theory -- PART I: THEORY -- 9.1 MINIMAX ESTIMATORS -- 9.2 MINIMUM RISK EQUIVARIANT, BAYES EQUIVARIANT, AND STRUCTURAL ESTIMATORS -- 9.2.1 Formal Bayes Estimators for Invariant Priors -- 9.2.2 Equivariant Estimators Based on Structural Distributions -- 9.3 THE ADMISSIBILITY OF ESTIMATORS -- 9.3.1 Some Basic Results -- 9.3.2 The Inadmissibility of Some Commonly Used Estimators -- 9.3.3 Minimax and Admissible Estimators of the Location Parameter -- 9.3.4 The Relationship of Empirical Bayes and Stein-Type Estimators of the Location Parameter in the Normal Case -- PART II: EXAMPLES -- PART III: PROBLEMS -- PART IV: SOLUTIONS OF SELECTED PROBLEMS -- References -- Author Index -- Subject Index -- WILEY SERIES IN PROBABILITY AND STATISTICS. |
| Record Nr. | UNINA-9910814694503321 |
|
Zacks Shelemyahu <1932->
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stage-wise adaptive designs [[electronic resource] /] / Shelemyahu Zacks
| Stage-wise adaptive designs [[electronic resource] /] / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, c2009 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 610.72 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Medicine - Research - Statistical methods
Medical statistics Statistics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-13750-6
9786612137501 0-470-46695-2 0-470-46694-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Stage-Wise Adaptive Designs; CONTENTS; Preface; 1 Synopsis; 1.1 Multistage and Sequential Estimation; 1.2 Adaptive Designs for Generalized Linear Models; 1.3 Adaptive Methods for Sampling from Finite Populations; 1.4 Adaptive Prediction and Forecasting in Time Series Analysis; 1.5 Adaptive Search of an MTD in Cancer Phase I Clinical Trials; 1.6 Adaptive and Sequential Procedures in Phase III Clinical Trials; 1.7 Sequential Allocation of Resources; 1.8 Sequential Detection of Change Points; 1.9 Sequential Methods in Industrial Testing, Reliability, and Design of Experiments
2 Multistage and Sequential Estimation2.1 Stein's Two-Stage Procedure; 2.2 Modifications to Attain Asymptotic Efficiency; 2.3 Two-Stage Sampling from Exponential Distributions; 2.3.1 Fixed-Width Confidence Interval for the Location Parameter of an Exponential Distribution; 2.3.2 Two-Stage Sampling for a Bounded Risk Point Estimation of the Exponential Parameter; 2.4 Sequential Fixed-Width Interval Estimation; 2.5 Distributions of Stopping Variables of Sequential Sampling; 2.5.1 General Theory; 2.5.2 Characteristics of Ray's Procedure; 2.5.3 Risk of Some Sequential Point Estimators 2.6 Sequential Fixed-Width Intervals for the Log-Odds in Bernoulli Trials2.6.1 Problem; 2.6.2 Distribution of N(δ); 2.6.3 Functionals of Pn(δ); 2.7 Bayesian Sequential Estimation; 2.7.1 General Theory; 2.7.2 Estimating the Scale Parameter of the Exponential Distribution; 3 Adaptive Designs for Generalized Linear Models; 3.1 Exponential Example; 3.2 Adaptive Designs for the Fisher Information; 3.3 Adaptive Bayesian Designs; 3.4 Adaptive Designs for Inverse Regression; 3.4.1 Non-Bayesian Adaptive Designs; 3.4.2 Bayesian Adaptive Designs, σ Known; 3.5 Stochastic Approximation 4 Adaptive Methods for Sampling from Finite Populations4.1 Basic Theory; 4.1.1 Design Approach; 4.1.2 Modeling Approach; 4.2 Two-Stage and Sequential Estimation of the Population Mean; 4.2.1 Design Approach: SRSWR; 4.2.2 Design Approach: SRSWOR; 4.2.3 Modeling Approach; 4.3 Adaptive Allocation of Stratified SRS; 4.3.1 Basic Theory; 4.3.2 Two-Stage Procedure for a Fixed-Width Interval Estimation of Yn Under Stratified Sampling; 4.4 Adaptive Search for Special Units; 4.5 Adaptive Estimation of the Size of a Finite Population; 4.6 Applications in Software Reliability 4.6.1 Sequential Stopping for Time Domain Models4.6.2 Sequential Stopping for Data Domain Models; 4.7 Sampling Inspection Schemes; 4.7.1 Two-Stage Sampling for Attributes; 4.7.2 Sequential Sampling for Attributes; 4.8 Dynamic Bayesian Prediction; 5 Adaptive Prediction and Forecasting in Time Series Analysis; 5.1 Basic Tools of Time Series Analysis; 5.2 Linear Predictors for Covariance Stationary T.S.; 5.2.1 Optimal Linear Predictors; 5.2.2 Minimal PMSE Predictors for AR(p) T.S.; 5.2.3 Prediction with Unknown Covariance Structure; 5.2.4 ARIMA Forecasting 5.3 Quadratic LSE Predictors for Nonstationary T.S. |
| Record Nr. | UNINA-9910139790503321 |
|
Zacks Shelemyahu <1932->
|
||
| Hoboken, NJ, : John Wiley & Sons, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stage-wise adaptive designs [[electronic resource] /] / Shelemyahu Zacks
| Stage-wise adaptive designs [[electronic resource] /] / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, c2009 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 610.72 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Medicine - Research - Statistical methods
Medical statistics Statistics |
| ISBN |
1-282-13750-6
9786612137501 0-470-46695-2 0-470-46694-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Stage-Wise Adaptive Designs; CONTENTS; Preface; 1 Synopsis; 1.1 Multistage and Sequential Estimation; 1.2 Adaptive Designs for Generalized Linear Models; 1.3 Adaptive Methods for Sampling from Finite Populations; 1.4 Adaptive Prediction and Forecasting in Time Series Analysis; 1.5 Adaptive Search of an MTD in Cancer Phase I Clinical Trials; 1.6 Adaptive and Sequential Procedures in Phase III Clinical Trials; 1.7 Sequential Allocation of Resources; 1.8 Sequential Detection of Change Points; 1.9 Sequential Methods in Industrial Testing, Reliability, and Design of Experiments
2 Multistage and Sequential Estimation2.1 Stein's Two-Stage Procedure; 2.2 Modifications to Attain Asymptotic Efficiency; 2.3 Two-Stage Sampling from Exponential Distributions; 2.3.1 Fixed-Width Confidence Interval for the Location Parameter of an Exponential Distribution; 2.3.2 Two-Stage Sampling for a Bounded Risk Point Estimation of the Exponential Parameter; 2.4 Sequential Fixed-Width Interval Estimation; 2.5 Distributions of Stopping Variables of Sequential Sampling; 2.5.1 General Theory; 2.5.2 Characteristics of Ray's Procedure; 2.5.3 Risk of Some Sequential Point Estimators 2.6 Sequential Fixed-Width Intervals for the Log-Odds in Bernoulli Trials2.6.1 Problem; 2.6.2 Distribution of N(δ); 2.6.3 Functionals of Pn(δ); 2.7 Bayesian Sequential Estimation; 2.7.1 General Theory; 2.7.2 Estimating the Scale Parameter of the Exponential Distribution; 3 Adaptive Designs for Generalized Linear Models; 3.1 Exponential Example; 3.2 Adaptive Designs for the Fisher Information; 3.3 Adaptive Bayesian Designs; 3.4 Adaptive Designs for Inverse Regression; 3.4.1 Non-Bayesian Adaptive Designs; 3.4.2 Bayesian Adaptive Designs, σ Known; 3.5 Stochastic Approximation 4 Adaptive Methods for Sampling from Finite Populations4.1 Basic Theory; 4.1.1 Design Approach; 4.1.2 Modeling Approach; 4.2 Two-Stage and Sequential Estimation of the Population Mean; 4.2.1 Design Approach: SRSWR; 4.2.2 Design Approach: SRSWOR; 4.2.3 Modeling Approach; 4.3 Adaptive Allocation of Stratified SRS; 4.3.1 Basic Theory; 4.3.2 Two-Stage Procedure for a Fixed-Width Interval Estimation of Yn Under Stratified Sampling; 4.4 Adaptive Search for Special Units; 4.5 Adaptive Estimation of the Size of a Finite Population; 4.6 Applications in Software Reliability 4.6.1 Sequential Stopping for Time Domain Models4.6.2 Sequential Stopping for Data Domain Models; 4.7 Sampling Inspection Schemes; 4.7.1 Two-Stage Sampling for Attributes; 4.7.2 Sequential Sampling for Attributes; 4.8 Dynamic Bayesian Prediction; 5 Adaptive Prediction and Forecasting in Time Series Analysis; 5.1 Basic Tools of Time Series Analysis; 5.2 Linear Predictors for Covariance Stationary T.S.; 5.2.1 Optimal Linear Predictors; 5.2.2 Minimal PMSE Predictors for AR(p) T.S.; 5.2.3 Prediction with Unknown Covariance Structure; 5.2.4 ARIMA Forecasting 5.3 Quadratic LSE Predictors for Nonstationary T.S. |
| Record Nr. | UNINA-9910831100503321 |
|
Zacks Shelemyahu <1932->
|
||
| Hoboken, NJ, : John Wiley & Sons, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stage-wise adaptive designs / / Shelemyahu Zacks
| Stage-wise adaptive designs / / Shelemyahu Zacks |
| Autore | Zacks Shelemyahu <1932-> |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, c2009 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 610.72 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Medicine - Research - Statistical methods
Medical statistics Statistics |
| ISBN |
1-282-13750-6
9786612137501 0-470-46695-2 0-470-46694-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Stage-Wise Adaptive Designs; CONTENTS; Preface; 1 Synopsis; 1.1 Multistage and Sequential Estimation; 1.2 Adaptive Designs for Generalized Linear Models; 1.3 Adaptive Methods for Sampling from Finite Populations; 1.4 Adaptive Prediction and Forecasting in Time Series Analysis; 1.5 Adaptive Search of an MTD in Cancer Phase I Clinical Trials; 1.6 Adaptive and Sequential Procedures in Phase III Clinical Trials; 1.7 Sequential Allocation of Resources; 1.8 Sequential Detection of Change Points; 1.9 Sequential Methods in Industrial Testing, Reliability, and Design of Experiments
2 Multistage and Sequential Estimation2.1 Stein's Two-Stage Procedure; 2.2 Modifications to Attain Asymptotic Efficiency; 2.3 Two-Stage Sampling from Exponential Distributions; 2.3.1 Fixed-Width Confidence Interval for the Location Parameter of an Exponential Distribution; 2.3.2 Two-Stage Sampling for a Bounded Risk Point Estimation of the Exponential Parameter; 2.4 Sequential Fixed-Width Interval Estimation; 2.5 Distributions of Stopping Variables of Sequential Sampling; 2.5.1 General Theory; 2.5.2 Characteristics of Ray's Procedure; 2.5.3 Risk of Some Sequential Point Estimators 2.6 Sequential Fixed-Width Intervals for the Log-Odds in Bernoulli Trials2.6.1 Problem; 2.6.2 Distribution of N(δ); 2.6.3 Functionals of Pn(δ); 2.7 Bayesian Sequential Estimation; 2.7.1 General Theory; 2.7.2 Estimating the Scale Parameter of the Exponential Distribution; 3 Adaptive Designs for Generalized Linear Models; 3.1 Exponential Example; 3.2 Adaptive Designs for the Fisher Information; 3.3 Adaptive Bayesian Designs; 3.4 Adaptive Designs for Inverse Regression; 3.4.1 Non-Bayesian Adaptive Designs; 3.4.2 Bayesian Adaptive Designs, σ Known; 3.5 Stochastic Approximation 4 Adaptive Methods for Sampling from Finite Populations4.1 Basic Theory; 4.1.1 Design Approach; 4.1.2 Modeling Approach; 4.2 Two-Stage and Sequential Estimation of the Population Mean; 4.2.1 Design Approach: SRSWR; 4.2.2 Design Approach: SRSWOR; 4.2.3 Modeling Approach; 4.3 Adaptive Allocation of Stratified SRS; 4.3.1 Basic Theory; 4.3.2 Two-Stage Procedure for a Fixed-Width Interval Estimation of Yn Under Stratified Sampling; 4.4 Adaptive Search for Special Units; 4.5 Adaptive Estimation of the Size of a Finite Population; 4.6 Applications in Software Reliability 4.6.1 Sequential Stopping for Time Domain Models4.6.2 Sequential Stopping for Data Domain Models; 4.7 Sampling Inspection Schemes; 4.7.1 Two-Stage Sampling for Attributes; 4.7.2 Sequential Sampling for Attributes; 4.8 Dynamic Bayesian Prediction; 5 Adaptive Prediction and Forecasting in Time Series Analysis; 5.1 Basic Tools of Time Series Analysis; 5.2 Linear Predictors for Covariance Stationary T.S.; 5.2.1 Optimal Linear Predictors; 5.2.2 Minimal PMSE Predictors for AR(p) T.S.; 5.2.3 Prediction with Unknown Covariance Structure; 5.2.4 ARIMA Forecasting 5.3 Quadratic LSE Predictors for Nonstationary T.S. |
| Record Nr. | UNINA-9910877825703321 |
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Zacks Shelemyahu <1932->
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| Hoboken, NJ, : John Wiley & Sons, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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