# Linear Models and Generalizations Least Squares and Alternatives

ISBN-10: 3540742263
ISBN-13: 9783540742265
Edition: 3rd 2008
Authors:
List price: $139.00 30 day, 100% satisfaction guarantee If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost. Learn more about our returns policy what's this? Rush Rewards U Members Receive: You have reached 400 XP and carrot coins. That is the daily max! ## Study Briefs Limited time offer: Get the first one free! (?) All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster. Add to cart Calculus 1 Online content$4.95 $1.99 Add to cart SQL Online content$4.95 $1.99 Add to cart MS Excel® 2010 Online content$4.95 $1.99 Add to cart MS Word® 2010 Online content$4.95 $1.99 ### Customers also bought #### Book details List price:$139.00
Edition: 3rd
Publisher: Springer
Publication date: 10/12/2007
Binding: Hardcover
Pages: 572
Size: 6.50" wide x 9.25" long x 1.50" tall
Weight: 2.2
Language: English

C. R. Rao, born in India, is one of this century's foremost statisticians, and received his education in statistics at the Indian Statistical Institute (ISI), Calcutta. He is Emeritus Holder of the Eberly Family Chair in Statistics at Penn State and Director of the Center for Multivariate Analysis. He has long been recognized as one of the world's top statisticians, and has been awarded 34 honorary doctorates from universities in 19 countries spanning 6 continents. His research has influenced not only statistics, but also the physical, social and natural sciences and engineering. In 2011 he was recipient of the Royal Statistical Society's Guy Medal in Gold which is awarded triennially to those "who are judged to have merited a signal mark of distinction by reason of their innovative contributions to the theory or application of statistics". It can be awarded both to fellows (members) of the Society and to non-fellows. Since its inception 120 years ago the Gold Medal has been awarded to 34 distinguished statisticians. The first medal was awarded to Charles Booth in 1892. Only two statisticians, H. Cramer (Norwegian) and J. Neyman (Polish), outside Great Britain were awarded the Gold medal and C. R. Rao is the first non-European and non-American to receive the award. Other awards he has received are the Gold Medal of Calcutta University, Wilks Medal of the American Statistical Association, Wilks Army Medal, Guy Medal in Silver of the Royal Statistical Society (UK), Megnadh Saha Medal and Srinivasa Ramanujan Medal of the Indian National Science Academy, J.C.Bose Gold Medal of Bose Institute and Mahalanobis Centenary Gold Medal of the Indian Science Congress, the Bhatnagar award of the Council of Scientific and Industrial Research, India and the Government of India honored him with the second highest civilian award, Padma Vibhushan, for "outstanding contributions to Science and Engineering / Statistics", and also instituted a cash award in honor of C R Rao, "to be given once in two years to a young statistician for work done during the preceding 3 years in any field of statistics". For his outstanding achievements Rao has been honored with the establishment of an institute named after him, C.R.Rao Advanced Institute for Mathematics, Statistics and Computer Science, in the campus of the University of Hyderabad, India.

 Preface to the First Edition Preface to the Second Edition Preface to the Third Edition Introduction Linear Models and Regression Analysis Plan of the Book The Simple Linear Regression Model The Linear Model Least Squares Estimation Direct Regression Method Properties of the Direct Regression Estimators Centered Model No Intercept Term Model Maximum Likelihood Estimation Testing of Hypotheses and Confidence Interval Estimation Analysis of Variance Goodness of Fit of Regression Reverse Regression Method Orthogonal Regression Method Reduced Major Axis Regression Method Least Absolute Deviation Regression Method Estimation of Parameters when X Is Stochastic The Multiple Linear Regression Model and Its Extensions The Linear Model The Principle of Ordinary Least Squares (OLS) Geometric Properties of OLS Best Linear Unbiased Estimation Basic Theorems Linear Estimators Mean Dispersion Error Estimation (Prediction) of the Error Term ï¿½ and ï¿½2 Classical Regression under Normal Errors The Maximum-Likelihood (ML) Principle Maximum Likelihood Estimation in Classical Normal Regression Consistency of Estimators Testing Linear Hypotheses Analysis of Variance Goodness of Fit Checking the Adequacy of Regression Analysis Univariate Regression Multiple Regression A Complex Example Graphical Presentation Linear Regression with Stochastic Regressors Regression and Multiple Correlation Coefficient Heterogenous Linear Estimation without Normality Heterogeneous Linear Estimation under Normality The Canonical Form Identification and Quantification of Multicollinearity Principal Components Regression Ridge Estimation Shrinkage Estimates Partial Least Squares Tests of Parameter Constancy The Chow Forecast Test The Hansen Test Tests with Recursive Estimation Test for Structural Change Total Least Squares Minimax Estimation Inequality Restrictions The Minimax Principle Censored Regression Overview LAD Estimators and Asymptotic Normality Tests of Linear Hypotheses Simultaneous Confidence Intervals Confidence Interval for the Ratio of Two Linear Parametric Functions Nonparametric Regression Estimation of the Regression Function Classification and Regression Trees (CART) Boosting and Bagging Projection Pursuit Regression Neural Networks and Nonparametric Regression Logistic Regression and Neural Networks Functional Data Analysis (FDA) Restricted Regression Problem of Selection Theory of Restricted Regression Efficiency of Selection Explicit Solution in Special Cases LINEX Loss Function Balanced Loss Function Complements Linear Models without Moments: Exercise Nonlinear Improvement of OLSE for Nonnormal Disturbances A Characterization of the Least Squares Estimator A Characterization of the Least Squares Estimator: A Lemma Exercises The Generalized Linear Regression Model Optimal Linear Estimation of ï¿½ R1-Optimal Estimators R2-Optimal Estimators R3-Optimal Estimators The Aitken Estimator Misspecification of the Dispersion Matrix Heteroscedasticity and Autoregression Mixed Effects Model: Unified Theory of Linear Estimation Mixed Effects Model A Basic Lemma Estimation of Xï¿½ (the Fixed Effect) Prediction of Uï¿½ (the Random Effect) Estimation of ϵ Linear Mixed Models with Normal Errors and Random Effects Maximum Likelihood Estimation of Linear Mixed Models Restricted Maximum Likelihood Estimation of Linear Mixed Models Inference for Linear Mixed Models Regression-Like Equations in Econometrics Econometric Models The Reduced Form The Multivariate Regression Model The Classical Multivariate Linear Regression Model Stochastic Regression Instrumental Variable Estimator Seemingly Unrelated Regressions Measurement Error Models Simultaneous Parameter Estimation by Empirical Bayes Solutions Overview Estimation of Parameters from Different Linear Models Supplements Gauss-Markov, Aitken and Rao Least Squares Estimators Gauss-Markov Least Squares Aitken Least Squares Rao Least Squares Exercises Exact and Stochastic Linear Restrictions Use of Prior Information The Restricted Least-Squares Estimator Maximum Likelihood Estimation under Exact Restrictions Stepwise Inclusion of Exact Linear Restrictions Biased Linear Restrictions and MDE Comparison with the OLSE MDE Matrix Comparisons of Two Biased Estimators MDE Matrix Comparison of Two Linear Biased Estimators MDE Comparison of Two (Biased) Restricted Estimators Stein-Rule Estimators under Exact Restrictions Stochastic Linear Restrictions Mixed Estimator Assumptions about the Dispersion Matrix Biased Stochastic Restrictions Stein-Rule Estimators under Stochastic Restrictions Weakened Linear Restrictions Weakly (R, r)-Unbiasedness Optimal Weakly (R, r)-Unbiased Estimators Feasible Estimators-Optimal Substitution of ï¿½ in <$>\hat {\beta}_1<$> (ï¿½, A) RLSE instead of the Mixed Estimator Exercises Prediction in the Generalized Regression Model Introduction Some Simple Linear Models The Constant Mean Model The Linear Trend Model Polynomial Models The Prediction Model Optimal Heterogeneous Prediction Optimal Homogeneous Prediction MDE Matrix Comparisons between Optimal and Classical Predictors Comparison of Classical and Optimal Prediction with Respect to the y* Superiority Comparison of Classical and Optimal Predictors with Respect to the X*ï¿½ Superiority Prediction Regions Concepts and Definitions On q-Prediction Intervals On q-Intervals in Regression Analysis On (p, q)-Prediction Intervals Linear Utility Functions Normally Distributed Populations - Two-Sided Symmetric Intervals Onesided Infinite Intervals Utility and Length of Intervals Utility and coverage Maximal Utility and Optimal Tests Prediction Ellipsoids Based on the GLSE Comparing the Efficiency of Prediction Ellipsoids Simultaneous Prediction of Actual and Average Values of y Specification of Target Function Exact Linear Restrictions MDEP Using Ordinary Least Squares Estimator MDEP Using Restricted Estimator MDEP Matrix Comparison Stein-Rule Predictor Outside Sample Predictions Kalman Filter Dynamical and Observational Equations Some Theorems Kalman Model Exercises Sensitivity Analysis Introduction Prediction Matrix Effect of Single Observation on Estimation of Parameters Measures Based on Residuals Algebraic Consequences of Omitting an Observation Detection of Outliers Diagnostic Plots for Testing the Model Assumptions Measures Based on the Confidence Ellipsoid Partial Regression Plots Regression Diagnostics for Removing an Observation with Graphics Model Selection Criteria Akaikes Information Criterion Bayesian Information Criterion Mallows Cp Example Exercises Analysis of Incomplete Data Sets Statistical Methods with Missing Data Complete Case Analysis Available Case Analysis Filling in the Missing Values Model-Based Procedures Missing-Data Mechanisms Missing Indicator Matrix Missing Completely at Random Missing at Random Nonignorable Nonresponse Missing Pattern Missing Data in the Response Least-Squares Analysis for Filled-up Data-Yates Procedure Analysis of Covariance-Bartlett's Method Shrinkage Estimation by Yates Procedure Shrinkage Estimators Efficiency Properties Missing Values in the X-Matrix General Model Missing Values and Loss in Efficiency Methods for Incomplete X-Matrices Complete Case Analysis Available Case Analysis Maximum-Likelihood Methods Imputation Methods for Incomplete X-Matrices Maximum-Likelihood Estimates of Missing Values Zero-Order Regression First-Order Regression Multiple Imputation Weighted Mixed Regression The Two-Stage WMRE Assumptions about the Missing Mechanism Regression Diagnostics to Identify Non-MCAR Processes Comparison of the Means Comparing the Variance-Covariance Matrices Diagnostic Measures from Sensitivity Analysis Distribution of the Measures and Test Procedure Treatment of Nonignorable Nonresponse Joint Distribution of (X,Y) with Missing Values Only in Y Conditional Distribution of Y Given X with Missing Values Only in Y Conditional Distribution of Y Given X with Missing Values Only in X Other Approaches Further Literature Exercises Robust Regression Overview Least Absolute Deviation Estimators - Univariate Case M-Estimates: Univariate Case Asymptotic Distributions of LAD Estimators Univariate Case Multivariate Case General M-Estimates Tests of Significance Models for Categorical Response Variables Generalized Linear Models Extension of the Regression Model Structure of the Generalized Linear Model Score Function and Information Matrix Maximum-Likelihood Estimation Testing of Hypotheses and Goodness of Fit Overdispersion Quasi Loglikelihood Contingency Tables Overview Ways of Comparing Proportions Sampling in Two-Way Contingency Tables Likelihood Function and Maximum-Likelihood Estimates Testing the Goodness of Fit GLM for Binary Response Logit Models and Logistic Regression Testing the Model Distribution Function as a Link Function Logit Models for Categorical Data Goodness of Fit-Likelihood-Ratio Test Loglinear Models for Categorical Variables Two-Way Contingency Tables Three-Way Contingency Tables The Special Case of Binary Response Coding of Categorical Explanatory Variables Dummy and Effect Coding Coding of Response Models Coding of Models for the Hazard Rate Extensions to Dependent Binary Variables Overview Modeling Approaches for Correlated Response Quasi-Likelihood Approach for Correlated Binary Response The GEE Method by Liang and Zeger Properties of the GEE Estimate <$>\hat {\beta}_G<$> Efficiency of the GEE and IEE Methods Choice of the Quasi-Correlation Matrix Rt(ï¿½) Bivariate Binary Correlated Response Variables The GEE Method The IEE Method An Example from the Field of Dentistry Full Likelihood Approach for Marginal Models Exercises Matrix Algebra Overview Trace of a Matrix Determinant of a Matrix Inverse of a Matrix Orthogonal Matrices Rank of a Matrix Range and Null Space Eigenvalues and Eigenvectors Decomposition of Matrices Definite Matrices and Quadratic Forms Idempotent Matrices Generalized Inverse Projectors Functions of Normally Distributed Variables Differentiation of Scalar Functions of Matrices Miscellaneous Results, Stochastic Convergence Tables Software for Linear Regression Models Software Special-Purpose Software Resources References Index

Free shipping on orders over $35* *A minimum purchase of$35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.