Wolfgang Karl Härdle Leopold Simar. Applied Multivariate. Statistical Analysis. Fourth Edition. ö Springer

Transcription

1 Wolfgang Karl Härdle Leopold Simar Applied Multivariate Statistical Analysis Fourth Edition ö Springer

2 Contents Part I Descriptive Techniques 1 Comparison of Batches Boxplots Histograms Kernel Densities Scatterplots Chernoff-Flury Faces Andrews'Curves Parallel Coordinates Plots Hexagon Plots Boston Housing Exercises 48 Part II Multivariate Random Variables 2 A Short Excursion into Matrix Algebra Elementary Operations Spectral Decompositions Quadratic Forms Derivatives Partitioned Matrices Geometrical Aspects Exercises 76 3 Moving to Higher Dimensions Covariance Correlation Summary Statistics Linear Model for Two Variables Simple Analysis of Variance 100 ix

3 x Contents 3.6 Multiple Linear Model Boston Housing HO 3.8 Exercises H3 4 Multivariate Distributions H7 4.1 Distribution and Density Function Moments and Characteristic Functions Transformations The Multinormal Distribution Sampling Distributions and Limit Theorems Heavy-Tailed Distributions Copulae Bootstrap Exercises Theory of the Multinormal Elementary Properties of the Multinormal The Wishart Distribution Hotelling's r 2 -Distribution Spherical and Elliptical Distributions Exercises Theory of Estimation The Likelihood Function The Cramer-Rao Lower Bound Exercises Hypothesis Testing Likelihood Ratio Test Linear Hypothesis Boston Housing Exercises 246 Part III Multivariate Techniques 8 Regression Models General ANOVA and ANCOVA Models ANOVA Models ANCOVA Models Boston Housing Categorical Responses Multinomial Sampling and Contingency Tables Log-Linear Models for Contingency Tables Testing Issues with Count Data Logit Models Exercises 279

4 Contents xi 9 Variable Selection Lasso Lasso in the Linear Regression Model Lasso in High Dimensions Lasso in Logit Model Elastic Net Elastic Net in Linear Regression Model Elastic Net in Logit Model Group Lasso Exercises Decomposition of Data Matrices by Factors The Geometrie Point of View Eitting the /J-Dimensional Point Cloud Fitting the n-dimensional Point Cloud Relations Between Subspaces Practica! Computation Exercises Principal Components Analysis Standardised Linear Combination Principal Components in Practice Interpretation of the PCs Asymptotic Properties of the PCs Normalised Principal Components Analysis Principal Components as a Factorial Method Common Principal Components Boston Housing MoreExamples Exercises Factor Analysis The Orthogonal Factor Model Estimation of the Factor Model Factor Scores and Strategies Boston Housing Exercises Cluster Analysis The Problem The Proximity Between Objects Cluster Algorithms Boston Housing Exercises 404

5 xij Contents 14 Discriminant Analysis Allocation Rules for Known Distributions Discrimination Rules in Practice Boston Housing Exercises Correspondence Analysis Motivation Chi-Square Decomposition Correspondence Analysis in Practice Exercises Canonical Correlation Analysis Most Interesting Linear Combination Canonical Correlation in Practice Exercises Multidimensional Scaling The Problem Metrie MDS NonmetricMDS Exercises Conjoint Measurement Analysis Introduction Design of Data Generation Estimation of Preference Orderings Exercises Applications in Finance Portfolio Choice Efficient Portfolio Efficient Portfolios in Practice The Capital Asset Pricing Model Exercises Computationally Intensive Techniques Simplicial Depth Projection Pursuit Sliced Inverse Regression Support Vector Machines Classification and Regression Trees Boston Housing Exercises 554

6 Contents xiii Part IV Appendix 21 Symbols and Notations Data Boston Housing Data Swiss Bank Notes CarData Classic Blue Pullovers Data US Companies Data French Food Data Car Marks French Baccalauröat Frequencies Journaux Data US Crime Data Plasma Data WAIS Data ANOVA Data Timebudget Data Geopol Data US Health Data Vocabulary Data Athletic Records Data Unemployment Data Annual Population Data Bankruptcy Data Bankruptcy Data II 571 References 573 Index 577