Applied Multivariate Statistical Analysis
Applied Multivariate Statistical Analysis
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DOI：
10.2307/2347962
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发表时间：
1983-06
期刊：
影响因子：
--
通讯作者：
Richard A. Johnson;D. W. Wichern
中科院分区：
文献类型：
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作者：
Richard A. Johnson;D. W. Wichern
(注：每章以导言开始，以练习和参考资料结束。)一、入门。1.多元分析的几个方面。多元技术的应用。数据的组织。数据显示和图形表示。距离。最后的评论。2.矩阵代数与随机向量。矩阵和向量代数的一些基础知识。正定矩阵。平方根矩阵。随机向量和矩阵。均值向量和协方差矩阵。矩阵不等式与极大化。附录A向量和矩阵：基本概念。3.样本几何和随机抽样。样例的几何图形。随机样本和样本均值和协方差矩阵的期望值。广义方差。样本均值、协方差和相关性作为矩阵运算。变量的线性组合的样本值。4.多元正态分布。多元正态密度及其性质多元正态分布的抽样和极大似然估计。‘X和S的抽样分布’X和S的大样本行为评估正态假设。检测大纲和数据清理。向接近常态的转变。关于多元均值和线性模型的推论。5.关于均值向量的推论。M0作为正态总体平均值的似然性。Hotling的T2检验和似然比检验。成分均值的置信域和同时比较。关于总体平均向量的大样本推断。多变量质量控制图。当某些观测值丢失时关于均值向量的推论。多变量观测中的时间依赖性带来的困难。补充5A同时置信度区间和椭圆作为p维椭球的阴影。6.几种多元均值的比较。配对比较和重复测量设计。比较两个总体的均值向量。几种多变量总体均值的比较(单向马诺瓦)。治疗效果的同时可信区间。双因素方差分析。轮廓分析。废除了措施、设计和增长曲线。视角和分析多变量模型的策略。7.多元线性回归模型。经典线性回归模型。最小二乘估计。关于回归模型的推论。从估计的回归函数中进行推断。模型检查和回归的其他方面。多元多元回归。线性回归的概念。比较回归模型的两种公式。具有时间依赖误差的多元回归模型。补充7A多元回归模型的似然比分布。三、A协方差结构分析。8.主成分。总体主成分。按主成分分类的样本差异汇总。绘制主成分图。大样本推论。用主成分监测质量。补充8A样本主成分近似的几何形状。9.结构协方差矩阵的因子分析与推断。正交因素模型。估算方法。因数旋转。因素得分。因素分析的视角和策略。结构方程模型。补充9A关于最大似然估计的一些计算细节。10.典型相关分析典型变量和典型相关。解释人口的典型变量。样本正则变量和样本正则相关。其他样本描述性措施。大样本推论。四、分类和分组技术。11.歧视和分类。两个种群的分离和分类。具有两个多元正态总体的分类。评估分类函数。费舍尔判别函数……种群的分离。用几个种群进行分类。费舍尔区分几个群体的方法。最后的评论。12.聚类、距离方法和排序。相似性度量。层次聚类法。非层次聚类方法。多维缩放。对应分析。用于查看样本单位和变量的双曲线图。性能分析：比较配置的一种方法。附录。标准正态概率。学生的t分布百分比。...c2分配百分比。F-分布百分比。F-分布百分比(...a=.10)。F-分布百分比(...a=0.05)。F-分布百分比(...a=.01)。数据索引。主题索引。
(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.