标题：生长曲线模型及其统计诊断
图书信息
出版社: 科学出版社; 第1版 (2007年8月1日)
丛书名: 数学专著系列(英文版)
精装: 387页
正文语种: 英语
开本: 16
ISBN: 9787030195326
条形码: 9787030195326
尺寸: 23.8 x 17.2 x 2.4 cm
重量: 798 g
内容简介
《生长曲线模型及其统计诊断》介绍生长曲线模型的理论及方法，并着重描述了该模型的统计诊断方法，主要内容包括：模型背景、资料介绍、参数估计理论、似然、诊断及贝尔叶斯诊断等，同时也介绍了大量的统计方法，讲述了生长曲线模型在医学、农业及生物等领域的广泛应用。《生长曲线模型及其统计诊断》适合医学、农业及生物领域内的数据分析者，应用统计工作者及从事统计学研究的人员及研究生参考阅读。
目录
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