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.
目錄：
Preface
Acronyms
Notation
Chapter 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 Readings
Chapter 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 Notes
Chapter 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 Notes
Chapter 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 Influence
Chapter 6 Bayesian Influence Assessment
Chapter 7 Baryesian Local Influence
Appendix
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