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Linear models in statistics [[electronic resource] /] / Alvin C. Rencher and G. Bruce Schaalje
Linear models in statistics [[electronic resource] /] / Alvin C. Rencher and G. Bruce Schaalje
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2008
Descrizione fisica 1 online resource (690 p.)
Disciplina 519.5/35
519.535
Altri autori (Persone) SchaaljeG. Bruce
Soggetto topico Linear models (Statistics)
ISBN 1-281-22163-5
9786611221638
0-470-19261-5
0-470-19260-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto LINEAR MODELS IN STATISTICS; CONTENTS; Preface; 1 Introduction; 1.1 Simple Linear Regression Model; 1.2 Multiple Linear Regression Model; 1.3 Analysis-of-Variance Models; 2 Matrix Algebra; 2.1 Matrix and Vector Notation; 2.1.1 Matrices, Vectors, and Scalars; 2.1.2 Matrix Equality; 2.1.3 Transpose; 2.1.4 Matrices of Special Form; 2.2 Operations; 2.2.1 Sum of Two Matrices or Two Vectors; 2.2.2 Product of a Scalar and a Matrix; 2.2.3 Product of Two Matrices or Two Vectors; 2.2.4 Hadamard Product of Two Matrices or Two Vectors; 2.3 Partitioned Matrices; 2.4 Rank; 2.5 Inverse
2.6 Positive Definite Matrices2.7 Systems of Equations; 2.8 Generalized Inverse; 2.8.1 Definition and Properties; 2.8.2 Generalized Inverses and Systems of Equations; 2.9 Determinants; 2.10 Orthogonal Vectors and Matrices; 2.11 Trace; 2.12 Eigenvalues and Eigenvectors; 2.12.1 Definition; 2.12.2 Functions of a Matrix; 2.12.3 Products; 2.12.4 Symmetric Matrices; 2.12.5 Positive Definite and Semidefinite Matrices; 2.13 Idempotent Matrices; 2.14 Vector and Matrix Calculus; 2.14.1 Derivatives of Functions of Vectors and Matrices; 2.14.2 Derivatives Involving Inverse Matrices and Determinants
2.14.3 Maximization or Minimization of a Function of a Vector3 Random Vectors and Matrices; 3.1 Introduction; 3.2 Means, Variances, Covariances, and Correlations; 3.3 Mean Vectors and Covariance Matrices for Random Vectors; 3.3.1 Mean Vectors; 3.3.2 Covariance Matrix; 3.3.3 Generalized Variance; 3.3.4 Standardized Distance; 3.4 Correlation Matrices; 3.5 Mean Vectors and Covariance Matrices for Partitioned Random Vectors; 3.6 Linear Functions of Random Vectors; 3.6.1 Means; 3.6.2 Variances and Covariances; 4 Multivariate Normal Distribution; 4.1 Univariate Normal Density Function
4.2 Multivariate Normal Density Function4.3 Moment Generating Functions; 4.4 Properties of the Multivariate Normal Distribution; 4.5 Partial Correlation; 5 Distribution of Quadratic Forms in y; 5.1 Sums of Squares; 5.2 Mean and Variance of Quadratic Forms; 5.3 Noncentral Chi-Square Distribution; 5.4 Noncentral F and t Distributions; 5.4.1 Noncentral F Distribution; 5.4.2 Noncentral t Distribution; 5.5 Distribution of Quadratic Forms; 5.6 Independence of Linear Forms and Quadratic Forms; 6 Simple Linear Regression; 6.1 The Model; 6.2 Estimation of β(0), β(1), and σ(2)
6.3 Hypothesis Test and Confidence Interval for β(1)6.4 Coefficient of Determination; 7 Multiple Regression: Estimation; 7.1 Introduction; 7.2 The Model; 7.3 Estimation of β and σ(2); 7.3.1 Least-Squares Estimator for β; 7.3.2 Properties of the Least-Squares Estimator β; 7.3.3 An Estimator for σ(2); 7.4 Geometry of Least-Squares; 7.4.1 Parameter Space, Data Space, and Prediction Space; 7.4.2 Geometric Interpretation of the Multiple Linear Regression Model; 7.5 The Model in Centered Form; 7.6 Normal Model; 7.6.1 Assumptions; 7.6.2 Maximum Likelihood Estimators for β and σ(2)
7.6.3 Properties of β and σ(2)
Record Nr. UNINA-9910144719203321
Rencher Alvin C. <1934->  
Hoboken, N.J., : Wiley-Interscience, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear models in statistics [[electronic resource] /] / Alvin C. Rencher and G. Bruce Schaalje
Linear models in statistics [[electronic resource] /] / Alvin C. Rencher and G. Bruce Schaalje
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2008
Descrizione fisica 1 online resource (690 p.)
Disciplina 519.5/35
519.535
Altri autori (Persone) SchaaljeG. Bruce
Soggetto topico Linear models (Statistics)
ISBN 1-281-22163-5
9786611221638
0-470-19261-5
0-470-19260-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto LINEAR MODELS IN STATISTICS; CONTENTS; Preface; 1 Introduction; 1.1 Simple Linear Regression Model; 1.2 Multiple Linear Regression Model; 1.3 Analysis-of-Variance Models; 2 Matrix Algebra; 2.1 Matrix and Vector Notation; 2.1.1 Matrices, Vectors, and Scalars; 2.1.2 Matrix Equality; 2.1.3 Transpose; 2.1.4 Matrices of Special Form; 2.2 Operations; 2.2.1 Sum of Two Matrices or Two Vectors; 2.2.2 Product of a Scalar and a Matrix; 2.2.3 Product of Two Matrices or Two Vectors; 2.2.4 Hadamard Product of Two Matrices or Two Vectors; 2.3 Partitioned Matrices; 2.4 Rank; 2.5 Inverse
2.6 Positive Definite Matrices2.7 Systems of Equations; 2.8 Generalized Inverse; 2.8.1 Definition and Properties; 2.8.2 Generalized Inverses and Systems of Equations; 2.9 Determinants; 2.10 Orthogonal Vectors and Matrices; 2.11 Trace; 2.12 Eigenvalues and Eigenvectors; 2.12.1 Definition; 2.12.2 Functions of a Matrix; 2.12.3 Products; 2.12.4 Symmetric Matrices; 2.12.5 Positive Definite and Semidefinite Matrices; 2.13 Idempotent Matrices; 2.14 Vector and Matrix Calculus; 2.14.1 Derivatives of Functions of Vectors and Matrices; 2.14.2 Derivatives Involving Inverse Matrices and Determinants
2.14.3 Maximization or Minimization of a Function of a Vector3 Random Vectors and Matrices; 3.1 Introduction; 3.2 Means, Variances, Covariances, and Correlations; 3.3 Mean Vectors and Covariance Matrices for Random Vectors; 3.3.1 Mean Vectors; 3.3.2 Covariance Matrix; 3.3.3 Generalized Variance; 3.3.4 Standardized Distance; 3.4 Correlation Matrices; 3.5 Mean Vectors and Covariance Matrices for Partitioned Random Vectors; 3.6 Linear Functions of Random Vectors; 3.6.1 Means; 3.6.2 Variances and Covariances; 4 Multivariate Normal Distribution; 4.1 Univariate Normal Density Function
4.2 Multivariate Normal Density Function4.3 Moment Generating Functions; 4.4 Properties of the Multivariate Normal Distribution; 4.5 Partial Correlation; 5 Distribution of Quadratic Forms in y; 5.1 Sums of Squares; 5.2 Mean and Variance of Quadratic Forms; 5.3 Noncentral Chi-Square Distribution; 5.4 Noncentral F and t Distributions; 5.4.1 Noncentral F Distribution; 5.4.2 Noncentral t Distribution; 5.5 Distribution of Quadratic Forms; 5.6 Independence of Linear Forms and Quadratic Forms; 6 Simple Linear Regression; 6.1 The Model; 6.2 Estimation of β(0), β(1), and σ(2)
6.3 Hypothesis Test and Confidence Interval for β(1)6.4 Coefficient of Determination; 7 Multiple Regression: Estimation; 7.1 Introduction; 7.2 The Model; 7.3 Estimation of β and σ(2); 7.3.1 Least-Squares Estimator for β; 7.3.2 Properties of the Least-Squares Estimator β; 7.3.3 An Estimator for σ(2); 7.4 Geometry of Least-Squares; 7.4.1 Parameter Space, Data Space, and Prediction Space; 7.4.2 Geometric Interpretation of the Multiple Linear Regression Model; 7.5 The Model in Centered Form; 7.6 Normal Model; 7.6.1 Assumptions; 7.6.2 Maximum Likelihood Estimators for β and σ(2)
7.6.3 Properties of β and σ(2)
Record Nr. UNINA-9910830151803321
Rencher Alvin C. <1934->  
Hoboken, N.J., : Wiley-Interscience, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear models in statistics / / Alvin C. Rencher and G. Bruce Schaalje
Linear models in statistics / / Alvin C. Rencher and G. Bruce Schaalje
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2008
Descrizione fisica 1 online resource (690 p.)
Disciplina 519.5/35
Altri autori (Persone) SchaaljeG. Bruce
Soggetto topico Linear models (Statistics)
ISBN 9786611221638
9781281221636
1281221635
9780470192610
0470192615
9780470192603
0470192607
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto LINEAR MODELS IN STATISTICS; CONTENTS; Preface; 1 Introduction; 1.1 Simple Linear Regression Model; 1.2 Multiple Linear Regression Model; 1.3 Analysis-of-Variance Models; 2 Matrix Algebra; 2.1 Matrix and Vector Notation; 2.1.1 Matrices, Vectors, and Scalars; 2.1.2 Matrix Equality; 2.1.3 Transpose; 2.1.4 Matrices of Special Form; 2.2 Operations; 2.2.1 Sum of Two Matrices or Two Vectors; 2.2.2 Product of a Scalar and a Matrix; 2.2.3 Product of Two Matrices or Two Vectors; 2.2.4 Hadamard Product of Two Matrices or Two Vectors; 2.3 Partitioned Matrices; 2.4 Rank; 2.5 Inverse
2.6 Positive Definite Matrices2.7 Systems of Equations; 2.8 Generalized Inverse; 2.8.1 Definition and Properties; 2.8.2 Generalized Inverses and Systems of Equations; 2.9 Determinants; 2.10 Orthogonal Vectors and Matrices; 2.11 Trace; 2.12 Eigenvalues and Eigenvectors; 2.12.1 Definition; 2.12.2 Functions of a Matrix; 2.12.3 Products; 2.12.4 Symmetric Matrices; 2.12.5 Positive Definite and Semidefinite Matrices; 2.13 Idempotent Matrices; 2.14 Vector and Matrix Calculus; 2.14.1 Derivatives of Functions of Vectors and Matrices; 2.14.2 Derivatives Involving Inverse Matrices and Determinants
2.14.3 Maximization or Minimization of a Function of a Vector3 Random Vectors and Matrices; 3.1 Introduction; 3.2 Means, Variances, Covariances, and Correlations; 3.3 Mean Vectors and Covariance Matrices for Random Vectors; 3.3.1 Mean Vectors; 3.3.2 Covariance Matrix; 3.3.3 Generalized Variance; 3.3.4 Standardized Distance; 3.4 Correlation Matrices; 3.5 Mean Vectors and Covariance Matrices for Partitioned Random Vectors; 3.6 Linear Functions of Random Vectors; 3.6.1 Means; 3.6.2 Variances and Covariances; 4 Multivariate Normal Distribution; 4.1 Univariate Normal Density Function
4.2 Multivariate Normal Density Function4.3 Moment Generating Functions; 4.4 Properties of the Multivariate Normal Distribution; 4.5 Partial Correlation; 5 Distribution of Quadratic Forms in y; 5.1 Sums of Squares; 5.2 Mean and Variance of Quadratic Forms; 5.3 Noncentral Chi-Square Distribution; 5.4 Noncentral F and t Distributions; 5.4.1 Noncentral F Distribution; 5.4.2 Noncentral t Distribution; 5.5 Distribution of Quadratic Forms; 5.6 Independence of Linear Forms and Quadratic Forms; 6 Simple Linear Regression; 6.1 The Model; 6.2 Estimation of β(0), β(1), and σ(2)
6.3 Hypothesis Test and Confidence Interval for β(1)6.4 Coefficient of Determination; 7 Multiple Regression: Estimation; 7.1 Introduction; 7.2 The Model; 7.3 Estimation of β and σ(2); 7.3.1 Least-Squares Estimator for β; 7.3.2 Properties of the Least-Squares Estimator β; 7.3.3 An Estimator for σ(2); 7.4 Geometry of Least-Squares; 7.4.1 Parameter Space, Data Space, and Prediction Space; 7.4.2 Geometric Interpretation of the Multiple Linear Regression Model; 7.5 The Model in Centered Form; 7.6 Normal Model; 7.6.1 Assumptions; 7.6.2 Maximum Likelihood Estimators for β and σ(2)
7.6.3 Properties of β and σ(2)
Record Nr. UNINA-9911019467103321
Rencher Alvin C. <1934->  
Hoboken, N.J., : Wiley-Interscience, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher, William F. Christensen
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher, William F. Christensen
Autore Rencher Alvin C. <1934->
Edizione [3rd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, c2012
Descrizione fisica 1 online resource (xxv, 758 p.) : ill
Disciplina 519.5/35
Altri autori (Persone) ChristensenWilliam F. <1970->
Collana Wiley series in probability and statistics
Soggetto topico Multivariate analysis
Anàlisi multivariable
Soggetto genere / forma Llibres electrònics
ISBN 1-118-39167-5
1-282-24188-5
9786613813008
1-118-39168-3
1-118-30458-6
1-118-39165-9
Classificazione MAT029020
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction; 2. Matrix Algebra; 3. Characterizing and Displaying Multivariate Data; 4. The Multivariate Normal Distribution; 5. Tests on One or Two Mean Vectors; 6. Multivariate Analysis of Variance; 7. Tests on Covariance Matrices; 8. Discriminant Analysis: Description of Group Separation; 9. Classification Analysis: Allocation of Observations to Groups; 10. Multivariate Regression; 11. Canonical Correlation; 12. Principal Component Analysis; 13. Exploratory Factor Analysis; 14. Confirmatory Factor Analysis; 15. Cluster Analysis; 16. Graphical Procedures; Appendix A: Tables; Appendix B: Answers and Hints to Problems; Appendix C: Data Sets and SAS Files; References; Index.
Record Nr. UNINA-9910141438803321
Rencher Alvin C. <1934->  
Hoboken, N.J., : Wiley, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Methods of multivariate analysis / / Alvin C. Rencher, William F. Christensen
Methods of multivariate analysis / / Alvin C. Rencher, William F. Christensen
Autore Rencher Alvin C. <1934->
Edizione [3rd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, c2012
Descrizione fisica 1 online resource (xxv, 758 p.) : ill
Disciplina 519.5/35
Altri autori (Persone) ChristensenWilliam F. <1970->
Collana Wiley series in probability and statistics
Soggetto topico Multivariate analysis
Anàlisi multivariable
Soggetto genere / forma Llibres electrònics
ISBN 9786613813008
9781118391679
1118391675
9781282241886
1282241885
9781118391686
1118391683
9781118304587
1118304586
9781118391655
1118391659
Classificazione MAT029020
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction; 2. Matrix Algebra; 3. Characterizing and Displaying Multivariate Data; 4. The Multivariate Normal Distribution; 5. Tests on One or Two Mean Vectors; 6. Multivariate Analysis of Variance; 7. Tests on Covariance Matrices; 8. Discriminant Analysis: Description of Group Separation; 9. Classification Analysis: Allocation of Observations to Groups; 10. Multivariate Regression; 11. Canonical Correlation; 12. Principal Component Analysis; 13. Exploratory Factor Analysis; 14. Confirmatory Factor Analysis; 15. Cluster Analysis; 16. Graphical Procedures; Appendix A: Tables; Appendix B: Answers and Hints to Problems; Appendix C: Data Sets and SAS Files; References; Index.
Record Nr. UNINA-9910822646203321
Rencher Alvin C. <1934->  
Hoboken, N.J., : Wiley, c2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa New York, : J. Wiley, 2002
Descrizione fisica 1 online resource (739 p.)
Disciplina 519.535
Collana Wiley series in probability and mathematical statistics
Soggetto topico Multivariate analysis
Mathematical statistics
Soggetto genere / forma Electronic books.
ISBN 1-280-36701-6
9786610367016
0-470-35680-4
0-471-46172-5
0-471-27135-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Methods of Multivariate Analysis Second Edition; Contents; Preface; Acknowledgments; 1. Introduction; 1.1 Why Multivariate Analysis?; 1.2 Prerequisites; 1.3 Objectives; 1.4 Basic Types of Data and Analysis; 2. Matrix Algebra; 2.1 Introduction; 2.2 Notation and Basic Definitions; 2.2.1 Matrices, Vectors, and Scalars; 2.2.2 Equality of Vectors and Matrices; 2.2.3 Transpose and Symmetric Matrices; 2.2.4 Special Matrices; 2.3 Operations; 2.3.1 Summation and Product Notation; 2.3.2 Addition of Matrices and Vectors; 2.3.3 Multiplication of Matrices and Vectors; 2.4 Partitioned Matrices; 2.5 Rank
2.6 Inverse2.7 Positive Definite Matrices; 2.8 Determinants; 2.9 Trace; 2.10 Orthogonal Vectors and Matrices; 2.11 Eigenvalues and Eigenvectors; 2.11.1 Definition; 2.11.2 I + A and I - A; 2.11.3 tr(A) and |A|; 2.11.4 Positive Definite and Semidefinite Matrices; 2.11.5 The Product AB; 2.11.6 Symmetric Matrix; 2.11.7 Spectral Decomposition; 2.11.8 Square Root Matrix; 2.11.9 Square Matrices and Inverse Matrices; 2.11.10 Singular Value Decomposition; 3. Characterizing and Displaying Multivariate Data; 3.1 Mean and Variance of a Univariate Random Variable
3.2 Covariance and Correlation of Bivariate Random Variables3.2.1 Covariance; 3.2.2 Correlation; 3.3 Scatter Plots of Bivariate Samples; 3.4 Graphical Displays for Multivariate Samples; 3.5 Mean Vectors; 3.6 Covariance Matrices; 3.7 Correlation Matrices; 3.8 Mean Vectors and Covariance Matrices for Subsets of Variables; 3.8.1 Two Subsets; 3.8.2 Three or More Subsets; 3.9 Linear Combinations of Variables; 3.9.1 Sample Properties; 3.9.2 Population Properties; 3.10 Measures of Overall Variability; 3.11 Estimation of Missing Values; 3.12 Distance between Vectors
4. The Multivariate Normal Distribution4.1 Multivariate Normal Density Function; 4.1.1 Univariate Normal Density; 4.1.2 Multivariate Normal Density; 4.1.3 Generalized Population Variance; 4.1.4 Diversity of Applications of the Multivariate Normal; 4.2 Properties of Multivariate Normal Random Variables; 4.3 Estimation in the Multivariate Normal; 4.3.1 Maximum Likelihood Estimation; 4.3.2 Distribution of y and S; 4.4 Assessing Multivariate Normality; 4.4.1 Investigating Univariate Normality; 4.4.2 Investigating Multivariate Normality; 4.5 Outliers; 4.5.1 Outliers in Univariate Samples
4.5.2 Outliers in Multivariate Samples5. Tests on One or Two Mean Vectors; 5.1 Multivariate versus Univariate Tests; 5.2 Tests on m with S Known; 5.2.1 Review of Univariate Test for H(0): m = m(0) with s Known; 5.2.2 Multivariate Test for H(0): m = m(0) with S Known; 5.3 Tests on m When S Is Unknown; 5.3.1 Review of Univariate t-Test for H(0): m = m(0) with s Unknown; 5.3.2 Hotelling's T(2)-Test for H(0): m = m(0) with S Unknown; 5.4 Comparing Two Mean Vectors; 5.4.1 Review of Univariate Two-Sample t-Test; 5.4.2 Multivariate Two-Sample T(2)-Test; 5.4.3 Likelihood Ratio Tests
5.5 Tests on Individual Variables Conditional on Rejection of H(0) by the T(2)-Test
Record Nr. UNINA-9910143174403321
Rencher Alvin C. <1934->  
New York, : J. Wiley, 2002
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher
Methods of multivariate analysis [[electronic resource] /] / Alvin C. Rencher
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa New York, : J. Wiley, 2002
Descrizione fisica 1 online resource (739 p.)
Disciplina 519.535
Collana Wiley series in probability and mathematical statistics
Soggetto topico Multivariate analysis
Mathematical statistics
ISBN 1-280-36701-6
9786610367016
0-470-35680-4
0-471-46172-5
0-471-27135-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Methods of Multivariate Analysis Second Edition; Contents; Preface; Acknowledgments; 1. Introduction; 1.1 Why Multivariate Analysis?; 1.2 Prerequisites; 1.3 Objectives; 1.4 Basic Types of Data and Analysis; 2. Matrix Algebra; 2.1 Introduction; 2.2 Notation and Basic Definitions; 2.2.1 Matrices, Vectors, and Scalars; 2.2.2 Equality of Vectors and Matrices; 2.2.3 Transpose and Symmetric Matrices; 2.2.4 Special Matrices; 2.3 Operations; 2.3.1 Summation and Product Notation; 2.3.2 Addition of Matrices and Vectors; 2.3.3 Multiplication of Matrices and Vectors; 2.4 Partitioned Matrices; 2.5 Rank
2.6 Inverse2.7 Positive Definite Matrices; 2.8 Determinants; 2.9 Trace; 2.10 Orthogonal Vectors and Matrices; 2.11 Eigenvalues and Eigenvectors; 2.11.1 Definition; 2.11.2 I + A and I - A; 2.11.3 tr(A) and |A|; 2.11.4 Positive Definite and Semidefinite Matrices; 2.11.5 The Product AB; 2.11.6 Symmetric Matrix; 2.11.7 Spectral Decomposition; 2.11.8 Square Root Matrix; 2.11.9 Square Matrices and Inverse Matrices; 2.11.10 Singular Value Decomposition; 3. Characterizing and Displaying Multivariate Data; 3.1 Mean and Variance of a Univariate Random Variable
3.2 Covariance and Correlation of Bivariate Random Variables3.2.1 Covariance; 3.2.2 Correlation; 3.3 Scatter Plots of Bivariate Samples; 3.4 Graphical Displays for Multivariate Samples; 3.5 Mean Vectors; 3.6 Covariance Matrices; 3.7 Correlation Matrices; 3.8 Mean Vectors and Covariance Matrices for Subsets of Variables; 3.8.1 Two Subsets; 3.8.2 Three or More Subsets; 3.9 Linear Combinations of Variables; 3.9.1 Sample Properties; 3.9.2 Population Properties; 3.10 Measures of Overall Variability; 3.11 Estimation of Missing Values; 3.12 Distance between Vectors
4. The Multivariate Normal Distribution4.1 Multivariate Normal Density Function; 4.1.1 Univariate Normal Density; 4.1.2 Multivariate Normal Density; 4.1.3 Generalized Population Variance; 4.1.4 Diversity of Applications of the Multivariate Normal; 4.2 Properties of Multivariate Normal Random Variables; 4.3 Estimation in the Multivariate Normal; 4.3.1 Maximum Likelihood Estimation; 4.3.2 Distribution of y and S; 4.4 Assessing Multivariate Normality; 4.4.1 Investigating Univariate Normality; 4.4.2 Investigating Multivariate Normality; 4.5 Outliers; 4.5.1 Outliers in Univariate Samples
4.5.2 Outliers in Multivariate Samples5. Tests on One or Two Mean Vectors; 5.1 Multivariate versus Univariate Tests; 5.2 Tests on m with S Known; 5.2.1 Review of Univariate Test for H(0): m = m(0) with s Known; 5.2.2 Multivariate Test for H(0): m = m(0) with S Known; 5.3 Tests on m When S Is Unknown; 5.3.1 Review of Univariate t-Test for H(0): m = m(0) with s Unknown; 5.3.2 Hotelling's T(2)-Test for H(0): m = m(0) with S Unknown; 5.4 Comparing Two Mean Vectors; 5.4.1 Review of Univariate Two-Sample t-Test; 5.4.2 Multivariate Two-Sample T(2)-Test; 5.4.3 Likelihood Ratio Tests
5.5 Tests on Individual Variables Conditional on Rejection of H(0) by the T(2)-Test
Record Nr. UNINA-9910830669903321
Rencher Alvin C. <1934->  
New York, : J. Wiley, 2002
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Methods of multivariate analysis / / Alvin C. Rencher
Methods of multivariate analysis / / Alvin C. Rencher
Autore Rencher Alvin C. <1934->
Edizione [2nd ed.]
Pubbl/distr/stampa New York, : J. Wiley, 2002
Descrizione fisica 1 online resource (739 p.)
Disciplina 519.535
Collana Wiley series in probability and mathematical statistics
Soggetto topico Multivariate analysis
Mathematical statistics
ISBN 9786610367016
9781280367014
1280367016
9780470356807
0470356804
9780471461722
0471461725
9780471271352
0471271357
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Methods of Multivariate Analysis Second Edition; Contents; Preface; Acknowledgments; 1. Introduction; 1.1 Why Multivariate Analysis?; 1.2 Prerequisites; 1.3 Objectives; 1.4 Basic Types of Data and Analysis; 2. Matrix Algebra; 2.1 Introduction; 2.2 Notation and Basic Definitions; 2.2.1 Matrices, Vectors, and Scalars; 2.2.2 Equality of Vectors and Matrices; 2.2.3 Transpose and Symmetric Matrices; 2.2.4 Special Matrices; 2.3 Operations; 2.3.1 Summation and Product Notation; 2.3.2 Addition of Matrices and Vectors; 2.3.3 Multiplication of Matrices and Vectors; 2.4 Partitioned Matrices; 2.5 Rank
2.6 Inverse2.7 Positive Definite Matrices; 2.8 Determinants; 2.9 Trace; 2.10 Orthogonal Vectors and Matrices; 2.11 Eigenvalues and Eigenvectors; 2.11.1 Definition; 2.11.2 I + A and I - A; 2.11.3 tr(A) and |A|; 2.11.4 Positive Definite and Semidefinite Matrices; 2.11.5 The Product AB; 2.11.6 Symmetric Matrix; 2.11.7 Spectral Decomposition; 2.11.8 Square Root Matrix; 2.11.9 Square Matrices and Inverse Matrices; 2.11.10 Singular Value Decomposition; 3. Characterizing and Displaying Multivariate Data; 3.1 Mean and Variance of a Univariate Random Variable
3.2 Covariance and Correlation of Bivariate Random Variables3.2.1 Covariance; 3.2.2 Correlation; 3.3 Scatter Plots of Bivariate Samples; 3.4 Graphical Displays for Multivariate Samples; 3.5 Mean Vectors; 3.6 Covariance Matrices; 3.7 Correlation Matrices; 3.8 Mean Vectors and Covariance Matrices for Subsets of Variables; 3.8.1 Two Subsets; 3.8.2 Three or More Subsets; 3.9 Linear Combinations of Variables; 3.9.1 Sample Properties; 3.9.2 Population Properties; 3.10 Measures of Overall Variability; 3.11 Estimation of Missing Values; 3.12 Distance between Vectors
4. The Multivariate Normal Distribution4.1 Multivariate Normal Density Function; 4.1.1 Univariate Normal Density; 4.1.2 Multivariate Normal Density; 4.1.3 Generalized Population Variance; 4.1.4 Diversity of Applications of the Multivariate Normal; 4.2 Properties of Multivariate Normal Random Variables; 4.3 Estimation in the Multivariate Normal; 4.3.1 Maximum Likelihood Estimation; 4.3.2 Distribution of y and S; 4.4 Assessing Multivariate Normality; 4.4.1 Investigating Univariate Normality; 4.4.2 Investigating Multivariate Normality; 4.5 Outliers; 4.5.1 Outliers in Univariate Samples
4.5.2 Outliers in Multivariate Samples5. Tests on One or Two Mean Vectors; 5.1 Multivariate versus Univariate Tests; 5.2 Tests on m with S Known; 5.2.1 Review of Univariate Test for H(0): m = m(0) with s Known; 5.2.2 Multivariate Test for H(0): m = m(0) with S Known; 5.3 Tests on m When S Is Unknown; 5.3.1 Review of Univariate t-Test for H(0): m = m(0) with s Unknown; 5.3.2 Hotelling's T(2)-Test for H(0): m = m(0) with S Unknown; 5.4 Comparing Two Mean Vectors; 5.4.1 Review of Univariate Two-Sample t-Test; 5.4.2 Multivariate Two-Sample T(2)-Test; 5.4.3 Likelihood Ratio Tests
5.5 Tests on Individual Variables Conditional on Rejection of H(0) by the T(2)-Test
Record Nr. UNINA-9911019726303321
Rencher Alvin C. <1934->  
New York, : J. Wiley, 2002
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