《生長曲線模型及其統計診斷》是科學出版社出版的一本圖書。適合醫學、農業及生物領域內的數據分析者，套用統計工作者及從事統計學研究的人員及研究生參考閱讀。
基本介紹
- 書名：生長曲線模型及其統計診斷
- 頁數：387頁
- 出版時間：第1版 (2007年8月1日)
- 裝幀：精裝
圖書信息,內容簡介,目錄,
圖書信息
出版社: 科學出版社;
叢書名: 數學專著系列(英文版)
:
正文語種: 英語
開本: 16
ISBN: 9787030195326
條形碼: 9787030195326
尺寸: 23.8 x 17.2 x 2.4 cm
重量: 798 g
內容簡介
《生長曲線模型及其統計診斷》介紹生長曲線模型的理論及方法，並著重描述了該模型的統計診斷方法，主要內容包括：模型背景、資料介紹、參數估計理論、似然、診斷及貝爾葉斯診斷等，同時也介紹了大量的統計方法，講述了生長曲線模型在醫學、農業及生物等領域的廣泛套用。
目錄
Preface
Acronyms
Notation
Chapter 1
Introduction
1.1 General Remarks
1.1.1 Statistical Diagnostics
1.1.2 Outliers 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
4.5 Influential Observation in the GCM with UC
4.5.1 Generalized Cook-type Distance
4.5.2 Confidence Ellipsoid's Volume
4.5.3 Influence Assessment on Linear Combination
4.5.4 Illustrative Examples
4.6 Bibliographical Notes
Chapter 5
Likelihood-Based Local Influence
5.1 General Remarks
5.1.1 Background
5.1.2 Local Influence Analysis
5.2 Local Influence Assessment in the GCM with SCS
5.2.1 Observed Information Matrix
5.2.2 Hessian Matrix
5.2.3 Covariance-Weighted Perturbation
5.2.4 Illustrative Examples
5.3 Local Influence Assessment in the GCM with UC
5.3.1 Observed Information Matrix
5.3.2 Hessian Matrix
5.3.3 Covariance-Weighted Perturbation
5.3.4 Illustrative Examples
5.4 Bibliographical Notes
Chapter 6
Bayesian Influence Assessment
6.1 General Remarks
6.1.1 Bayesian Influence Analysis
6.1.2 Kullback-Leibler Divergence
6.2 Bayesian Influence Analysis in the GCM with SCS
6.2.1 Posterior Distribution
6.2.2 Bayesian Influence Measurement
6.2.3 Illustrative Examples
6.3 Bayesian Influence Analysis in the GCM with UC
6.3.1 Posterior Distribution
6.3.2 Bayesian Influence Measurement
6.3.3 Illustrative Examples
6.4 Bibliographical Notes
Chapter 7
Bayesian Local Influence
7.1 General Remarks
7.1.1 Bayesian Local Influence
7.1.2 Bayesian Hessian Matrix
7.2 Bayesian Local Influence in the GCM with SCS
7.2.1 Bayesian Hessian Matrix
7.2.2 Covariance-Weighted Perturbation
7.2.3 Illustrative Examples
7.3 Bayesian Local Influence in the GCM with UC
7.3.1 Bayesian Hessian Matrix
7.3.2 Covariance-Weighted Perturbation
7.3.3 Illustrative Examples
7.4 Bibliographical Notes
Appendix
Data sets used in this book
References
Author Index
Subject Index
