Applied Multivariate Statistical Analysis

by Hardle, Wolfgang; Simar, Leopold

• ISBN13: 9783540030799
• ISBN10: 3540030794
• Format: Paperback
• Copyright: 2003-09-01
• Publisher: Springer Verlag

Summary

1Most of the observable phenomena in the empirical sciences are of multivariate nature. This book presents the tools and concepts of multivariate data analysis with a strong focus on applications. The text is devided into three parts. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents from a theoretical point of view distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide basket of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.

Author Biography

Leopold Simar is Professor of Statistics at The Universite Catholique de Louvain, Louvain-la-Neuve, Belgium where he is the Founder-Chairman of the Institute of Statistics.

Table of Contents

I Descriptive Techniques	11	(44)
1 Comparison of Batches	13	(42)
1.1 Boxplots	14	(8)
1.2 Histograms	22	(3)
1.3 Kernel Densities	25	(5)
1.4 Scatterplots	30	(4)
1.5 Chernoff-Flury Faces	34	(5)
1.6 Andrews' Curves	39	(3)
1.7 Parallel Coordinates Plots	42	(2)
1.8 Boston Housing	44	(8)
1.9 Exercises	52	(3)
II Multivariate Random Variables	55	(162)
2 A Short Excursion into Matrix Algebra	57	(24)
2.1 Elementary Operations	57	(6)
2.2 Spectral Decompositions	63	(2)
2.3 Quadratic Forms	65	(3)
2.4 Derivatives	68	(1)
2.5 Partitioned Matrices	68	(3)
2.6 Geometrical Aspects	71	(8)
2.7 Exercises	79	(2)
3 Moving to Higher Dimensions	81	(38)
3.1 Covariance	82	(4)
3.2 Correlation	86	(6)
3.3 Summary Statistics	92	(3)
3.4 Linear Model for Two Variables	95	(8)
3.5 Simple Analysis of Variance	103	(5)
3.6 Multiple Linear Model	108	(4)
3.7 Boston Housing	112	(3)
3.8 Exercises	115	(4)
4 Multivariate Distributions	119	(36)
4.1 Distribution and Density Function	120	(5)
4.2 Moments and Characteristic Functions	125	(10)
4.3 Transformations	135	(2)
4.4 The Multinormal Distribution	137	(5)
4.5 Sampling Distributions and Limit Theorems	142	(6)
4.6 Bootstrap	148	(4)
4.7 Exercises	152	(3)
5 Theory of the Multinormal	155	(18)
5.1 Elementary Properties of the Multinormal	155	(7)
5.2 The Wishart Distribution	162	(3)
5.3 Hotelting Distribution	165	(2)
5.4 Spherical and Elliptical Distributions	167	(2)
5.5 Exercises	169	(4)
6 Theory of Estimation	173	(10)
6.1 The Likelihood Function	174	(4)
6.2 The Cramer-Rao Lower Bound	178	(3)
6.3 Exercises	181	(2)
7 Hypothesis Testing	183	(34)
7.1 Likelihood Ratio Test	184	(8)
7.2 Linear Hypothesis	192	(17)
7.3 Boston Housing	209	(3)
7.4 Exercises	212	(5)
III Multivariate Techniques	217	(226)
8 Decomposition of Data Matrices by Factors	219	(14)
8.1 The Geometric Point of View	220	(1)
8.2 Fitting the p-dimensional Point Cloud	221	(4)
8.3 Fitting the n-dimensional Point Cloud	225	(2)
8.4 Relations between Subspaces	227	(1)
8.5 Practical Computation	228	(4)
8.6 Exercises	232	(1)
9 Principal Components Analysis	233	(42)
9.1 Standardized Linear Combinations	234	(4)
9.2 Principal Components in Practice	238	(3)
9.3 Interpretation of the PCs	241	(5)
9.4 Asymptotic Properties of the PCs	246	(3)
9.5 Normalized Principal Components Analysis	249	(1)
9.6 Principal Components as a Factorial Method	250	(6)
9.7 Common Principal Components	256	(3)
9.8 Boston Housing	259	(2)
9.9 More Examples	261	(11)
9.10 Exercises	272	(3)
10 Factor Analysis	275	(26)
10.1 The Orthogonal Factor Model	275	(7)
10.2 Estimation of the Factor Model	282	(9)
10.3 Factor Scores and Strategies	291	(2)
10.4 Boston Housing	293	(5)
10.5 Exercises	298	(3)
11 Cluster Analysis	301	(22)
11.1 The Problem	301	(1)
11.2 The Proximity between Objects	302	(6)
11.3 Cluster Algorithms	308	(8)
11.4 Boston Housing	316	(2)
11.5 Exercises	318	(5)
12 Discriminant Analysis	323	(18)
12.1 Allocation Rules for Known Distributions	323	(8)
12.2 Discrimination Rules in Practice	331	(6)
12.3 Boston Housing	337	(2)
12.4 Exercises	339	(2)
13 Correspondence Analysis	341	(20)
13.1 Motivation	341	(3)
13.2 Chi-square Decomposition	344	(3)
13.3 Correspondence Analysis in Practice	347	(11)
13.4 Exercises	358	(3)
14 Canonical Correlation Analysis	361	(12)
14.1 Most Interesting Linea Combination	361	(5)
14.2 Canonical Correlation in Practice	366	(6)
14.3 Exercise	372	(1)
15 Multidimensional Scaling	373	(20)
15.1 The Problem	373	(6)
15.2 Metric Multidimensional Scaling	379	(4)
15.2.1 The Classical Solution	379	(4)
15.3 Nonmetric Multidimensional Scaling	383	(8)
15.3.1 Shepard-Kruskal algorithm	384	(7)
15.4 Exercises	391	(2)
16 Conjoint Measurement Analysis	393	(14)
16.1 Introduction	393	(2)
16.2 Design of Data Generation	395	(3)
16.3Estimation of Preference Orderings	398	(7)
16.4 Exercises	405	(2)
17 Applications in Finance	407	(14)
17.1 Portfolio Choice	407	(1)
17.2 Efficient Portfolio	408	(7)
17.3 Efficient Portfolios in Practice	415	(2)
17.4 The Capital Asset Pricing Model (CAPM)	417	(1)
17.5 Exercises	418	(3)
18 Highly Interactive, Computationally Intensive Techniques	421	(26)
18.1 Simplicial Depth	421	(4)
18.2 Projection Pursuit	425	(6)
18.3 Sliced Inverse Regression	431	(8)
18.4 Boston Housing	439	(1)
18.5 Exercise	440	(3)
A Symbols and Notation	443	(4)
B Data	447	(32)
B.1 Boston Housing Data	447	(1)
B.2 Swiss Bank Notes	448	(4)
B.3 Car Data	452	(2)
B.4 Classic Blue Pullovers Data	454	(1)
B.5 U.S. Companies Data	455	(2)
B.6 French Food Data	457	(1)
B.7 Car Marks	458	(1)
B.8 French Baccalauréat Frequencies	459	(1)
B.9 Journaux Data	460	(1)
B.10 U.S. Crime Data	461	(2)
B.11 Plasma Data	463	(1)
B.12 WAIS Data	464	(2)
B.13 ANOVA Data	466	(1)
B.14 Timebudget Data	467	(2)
B.15 Geopol Data	469	(2)
B.16 U.S. Health Data	471	(2)
B.17 Vocabulary Data	473	(2)
B.18 Athletic Records Data	475	(2)
B.19 Unemployment Data	477	(1)
B.20 Annual Population Data	478	(1)
Bibliography	479	(4)
Index	483