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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 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-9910876860903321
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 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-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 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-9910877249103321
Rencher Alvin C. <1934->  
New York, : J. Wiley, 2002
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