Linear Models in Statistics

Name: Linear Models in Statistics
Price: 63.87 USD
Availability: InStock
ISBN: 9780471754985

ISBN-10: 0471754986

ISBN-13: 9780471754985

Edition: 2nd 2008

Authors: Alvin C. Rencher, G. Bruce Schaalje

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Description:

Linear Models in Statistics, Second Edition discusses classical linear models from a matrix algebra perspective, making the subject easily accessible to readers encountering linear models for the first time. It provides a solid foundation from which to explore the literature and interpret correctly the output of computer packages. It brings together a number of approaches to regression and analysis of variance from which more experienced practitioners will also benefit. With an emphasis on broad coverage of essential topics, this book clearly and carefully develops the basic theory of regression and analysis of variance, illustrating it with examples from a wide range of disciplines.

Book details

List price: $194.95
Edition: 2nd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/2/2008
Binding: Hardcover
Pages: 688
Size: 6.50" wide x 9.40" long x 1.70" tall
Weight: 2.684
Language: English

Alvin C. Rencher, PhD, is Professor of Statistics at Brigham Young University. Dr. Rencher is a Fellow of the American Statistical Association and the author of Methods of Multivariate Analysis and Multivariate Statistical Inference and Applications, both published by Wiley.G. Bruce Schaalje, PhD, is Professor of Statistics at Brigham Young University. He has authored over 120 journal articles in his areas of research interest, which include mixed linear models, small sample inference, and design of experiments.



Preface



Introduction



Simple Linear Regression Model



Multiple Linear Regression Model



Analysis-of-Variance Models



Matrix Algebra



Matrix and Vector Notation



Matrices, Vectors, and Scalars



Matrix Equality



Transpose



Matrices of Special Form



Operations



Sum of Two Matrices or Two Vectors



Product of a Scalar and a Matrix



Product of Two Matrices or Two Vectors



Hadamard Product of Two Matrices or Two Vectors



Partitioned Matrices



Rank



Inverse



Positive Definite Matrices



Systems of Equations



Generalized Inverse



Definition and Properties



Generalized Inverses and Systems of Equations



Determinants



Orthogonal Vectors and Matrices



Trace



Eigenvalues and Eigenvectors



Definition



Functions of a Matrix



Products



Symmetric Matrices



Positive Definite and Semidefinite Matrices



Idempotent Matrices



Vector and Matrix Calculus



Derivatives of Functions of Vectors and Matrices



Derivatives Involving Inverse Matrices and Determinants



Maximization or Minimization of a Function of a Vector



Random Vectors and Matrices



Introduction



Means, Variances, Covariances, and Correlations



Mean Vectors and Covariance Matrices for Random Vectors



Mean Vectors



Covariance Matrix



Generalized Variance



Standardized Distance



Correlation Matrices



Mean Vectors and Covariance Matrices for Partitioned Random Vectors



Linear Functions of Random Vectors



Means



Variances and Covariances



Multivariate Normal Distribution



Univariate Normal Density Function



Multivariate Normal Density Function



Moment Generating Functions



Properties of the Multivariate Normal Distribution



Partial Correlation



Distribution of Quadratic Forms in y



Sums of Squares



Mean and Variance of Quadratic Forms



Noncentral Chi-Square Distribution



Noncentral F and t Distributions



Noncentral F Distribution



Noncentral t Distribution



Distribution of Quadratic Forms



Independence of Linear Forms and Quadratic Forms



Simple Linear Regression



The Model



Estimation of [beta subscript 0], [beta subscript 1], and [sigma superscript 2]



Hypothesis Test and Confidence Interval for [beta subscript 1]



Coefficient of Determination



Multiple Regression: Estimation



Introduction



The Model



Estimation of [beta] and [sigma superscript 2]



Least-Squares Estimator for [beta]



Properties of the Least-Squares Estimator [beta]



An Estimator for [sigma superscript 2]



Geometry of Least-Squares



Parameter Space, Data Space, and Prediction Space



Geometric Interpretation of the Multiple Linear Regression Model



The Model in Centered Form



Normal Model



Assumptions



Maximum Likelihood Estimators for [beta] and [sigma superscript 2]



Properties of [beta] and [sigma superscript 2]



R[superscript 2] in Fixed-x Regression



Generalized Least-Squares: cov(y) = [sigma superscript 2]V



Estimation of [beta] and [sigma superscript 2] when cov(y) = [sigma superscript 2]V



Misspecification of the Error Structure



Model Misspecification



Orthogonalization



Multiple Regression: Tests of Hypotheses and Confidence Intervals



Test of Overall Regression



Test on a Subset of the [beta] Values



F Test in Terms of R[superscript 2]



The General Linear Hypothesis Tests for H[subscript 0]: C[beta] = 0 and H[subscript 0]: C[beta] = t



The Test for H[subscript 0]: C[beta] = 0



The Test for H[subscript 0]: C[beta] = t



Tests on [beta subscript j] and a' [beta]



Testing One [beta subscript j] or One a' [beta]



Testing Several [beta subscript j] or a'[subscript i beta] Values



Confidence Intervals and Prediction Intervals



Confidence Region for [beta]



Confidence Interval for [beta subscript j]



Confidence Interval for a'[beta]



Confidence Interval for E(y)



Prediction Interval for a Future Observation



Confidence Interval for [sigma superscript 2]



Simultaneous Intervals



Likelihood Ratio Tests



Multiple Regression: Model Validation and Diagnostics



Residuals



The Hat Matrix



Outliers



Influential Observations and Leverage



Multiple Regression: Random x's



Multivariate Normal Regression Model



Estimation and Testing in Multivariate Normal Regression



Standardized Regression Coefficients



R[superscript 2] in Multivariate Normal Regression



Tests and Confidence Intervals for R[superscript 2]



Effect of Each Variable on R[superscript 2]



Prediction for Multivariate Normal or Nonnormal Data



Sample Partial Correlations



Multiple Regression: Bayesian Inference



Elements of Bayesian Statistical Inference



A Bayesian Multiple Linear Regression Model



A Bayesian Multiple Regression Model with a Conjugate Prior



Marginal Posterior Density of [beta]



Marginal Posterior Densities of [tau] and [sigma superscript 2]



Inference in Bayesian Multiple Linear Regression



Bayesian Point and Interval Estimates of Regression Coefficients



Hypothesis Tests for Regression Coefficients in Bayesian Inference



Special Cases of Inference in Bayesian Multiple Regression Models



Bayesian Point and Interval Estimation of [sigma superscript 2]



Bayesian Inference through Markov Chain Monte Carlo Simulation



Posterior Predictive Inference



Analysis-of-Variance Models



Non-Full-Rank Models



One-Way Model



Two-Way Model



Estimation



Estimation of [beta]



Estimable Functions of [beta]



Estimators



Estimators of [lambda]'[beta]



Estimation of [sigma superscript 2]



Normal Model



Geometry of Least-Squares in the Overparameterized Model



Reparameterization



Side Conditions



Testing Hypotheses



Testable Hypotheses



Full-Reduced-Model Approach



General Linear Hypothesis



An Illustration of Estimation and Testing



Estimable Functions



Testing a Hypothesis



Orthogonality of Columns of X



One-Way Analysis-of-Variance: Balanced Case



The One-Way Model



Estimable Functions



Estimation of Parameters



Solving the Normal Equations



An Estimator for [sigma superscript 2]



Testing the Hypothesis H[subscript 0]: [mu subscript 1] = [mu subscript 2] = ... = [mu subscript k]



Full-Reduced-Model Approach



General Linear Hypothesis



Expected Mean Squares



Full-Reduced-Model Approach



General Linear Hypothesis



Contrasts



Hypothesis Test for a Contrast



Orthogonal Contrasts



Orthogonal Polynomial Contrasts



Two-Way Analysis-of-Variance: Balanced Case



The Two-Way Model



Estimable Functions



Estimators of [lambda]'[beta] and [sigma superscript 2]



Solving the Normal Equations and Estimating [lambda]'[beta]



An Estimator for [sigma superscript 2]



Testing Hypotheses



Test for Interaction



Tests for Main Effects



Expected Mean Squares



Sums-of-Squares Approach



Quadratic Form Approach



Analysis-of-Variance: The Cell Means Model for Unbalanced Data



Introduction



One-Way Model



Estimation and Testing



Contrasts



Two-Way Model



Unconstrained Model



Constrained Model



Two-Way Model with Empty Cells



Analysis-of-Covariance



Introduction



Estimation and Testing



The Analysis-of-Covariance Model



Estimation



Testing Hypotheses



One-Way Model with One Covariate



The Model



Estimation



Testing Hypotheses



Two-Way Model with One Covariate



Tests for Main Effects and Interactions



Test for Slope



Test for Homogeneity of Slopes



One-Way Model with Multiple Covariates



The Model



Estimation



Testing Hypotheses



Analysis-of-Covariance with Unbalanced Models



Linear Mixed Models



Introduction



The Linear Mixed Model



Examples



Estimation of Variance Components



Inference for [beta]



An Estimator for [beta]



Large-Sample Inference for Estimable Functions of [beta]



Small-Sample Inference for Estimable Functions of [beta]



Inference for the a[subscript i] Terms



Residual Diagnostics



Additional Models



Nonlinear Regression



Logistic Regression



Loglinear Models



Poisson Regression



Generalized Linear Models



Answers and Hints to the Problems


References


Index