生長曲線模型及其統(tǒng)計診斷

內(nèi)容概要

This book discusses the theory of a growth curve model (GCM) with particular emphasis on tatistical diagnostics, which is mainly based on recent work on diagnostics made by the authors and their collaborators. This book is intended for researchers who are working in the area of theoretical studies related to the GCM as well as multivariate statistical diagnostics, and for applied statisticians working in application of the GCM to practical areas.

書籍目錄

PrefaceAcronymsNotationChapter 1 Introduction　1.1 General Remarks　　1.1.1 Statistical Diagnostics　　1.1.20utliers and Influential Observation　1.2 Statistical Diagnostics in Multivariate Analysis　　1.2.1 Multiple Outliers in Multivariate Data　　1.2.2 Statistical diagnostics in multivariate models　1.3 Growth Curve Model (GCM)　　1.3.1 A Brief Review　　1.3.2 Covariance Structure Selection　1.4 Summary　　1.4.1 Statistical Inference　　1.4.2 Diagnostics Within a Iikelihood Framework　　1.4.3 Diagnostics Within a Bayesian Framework 　1.5 Preliminary Results　　1.5.1 Matrix Operation and Matrix Derivative　　1.5.2 Matrix-variate Normal and t Distributions 　1.6 Further ReadingsChapter 2 Generalized Least Square Estimation　2.1 General Remarks　　2.1.1 Model Definition　　2.1.2 Practical Examples　2.2 Generalized Least Square Estimation　　2.2.1 Generalized Least Square Estimate (GLSE) 　　2.2.2 Best Linear Unbiased Estimate (BLUE)　　2.2.3 Illustrative Examples　2.3 Admissible Estimate of Regression Coefficient　　2.3.1 Admissibility　　2.3.2 Necessary and Sufficient Condition　2.4 Bibliographical NotesChapter 3 Maximum Likelihood Estimation　3.1 Maximum Likelihood Estimation　　3.1.1 Maximum Likelihood Estimate (MLE)　　3.1.2 Expectation and Variance-covariance　　3.1.3 Illustrative Examples　3.2 Rao's Simple Covariance Structure (SCS)　　3.2.1 Condition That the MLE Is Identical to the GLSE　　3.2.2 Estimates of Dispersion Components　　3.2.3 Illustrative Examples　3.3 Restricted Maximum Likelihood Estimation　　3.3.1 Restricted Maximum Likelihood (REMLs) estimate 　　3.3.2 REMLs Estimates in the GCM　　3.3.3 Illustrative Examples　3.4 Bibliographical NotesChapter 4 Discordant Outlier and Influential Observation　4.1 General Remarks　　4.1.1 Discordant Outlier-Generating Model　　4.1.2 Influential Observation　4.2 Discordant Outlier Detection in the GCM with SCS　　4.2.1 Multiple Individual Deletion Model (MIDM)　　4.2.2 Mean Shift Regression Model (MSRM)　　4.2.3 Multiple Discordant Outlier Detection　　4.2.4 Illustrative Examples　4.3 Influential Observation in the GCM with SCS　　4.3.1 Generalized Cook-type Distance　　4.3.2 Confidence Ellipsoid's Volume　　4.3.3 Influence Assessment on Linear Combination　　4.3.4 Illustrative Examples　4.4 Discordant Outlier Detection in the GCM with UC　　4.4.1 Multiple Individual Deletion Model (MIDM)　　4.4.2 Mean Shift Regression Model (MSRM)　　4.4.3 Multiple Discordant Outlier Detection　　4.4.4 Illustrative Examples……Chapter 5 Likelihood-Based Local InfluenceChapter 6 Bayesian Influence AssessmentChapter 7 Baryesian Local InfluenceAppendix

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