Beschreibung
During the last twenty years multivariate statistical methods have become increasingly popular among scientists in various fields. The theory had already made great progress in previous decades and routine applications of multivariate methods followed with the advent of fast computers. Nowadays statistical software packages perform in seconds what used to take weeks of tedious calculations. Although this is certainly a welcome development, we find, on the other hand, that many users of statistical packages are not too sure of what they are doing, and this is especially true for multivariate statistical methods. Many researchers have heard about such techniques and feel intuitively that multivariate methods could be useful for their own work, but they haven't mastered the usual mathematical prerequisites. This book tries to fill the gap by explaining - in words and graphs - some basic concepts and selected methods of multivariate statistical analysis. Why another book? Are the existing books on applied multivariate statistics all obsolete? No, some of them are up to date and, indeed, quite good.
Inhalt
Preface.- 1 The data.- Discussion.- 2 Univariate plots and descriptive statistics.- Discussion.- Further study.- 3 Scatterplot, correlation and covariance.- Discussion.- Further study.- 4 Face plots.- Discussion.- Further study.- 5 Multiple linear regression.- 5.1 Introductory remarks.- 5.2 The model of multiple linear regression.- 5.3 Least squares estimation.- 5.4 Residual analysis.- 5.5 Model building, analysis of variance.- 5.6 The overall test of significance.- 5.7 Coefficient of determination and multiple correlation.- 5.8 Tests of partial hypotheses.- 5.9 Standard errors of the regression coefficients.- 5.10 Selection of a subset of regressors.- Discussion.- Further study.- 6 Linear combinations.- 6.1 Introduction.- 6.2 A special linear combination.- 6.3 Linear combinations of two variables.- 6.4 Linear combinations of several variables.- 6.5 Mean and standard deviation of linear combinations.- Discussion.- Further study.- 7 Linear discriminant analysis for two groups.- 7.1 Introduction.- 7.2 Multivariate standard distance.- 7.3 Relationship between discriminant analysis and multiple linear regression.- 7.4 Testing hypotheses about the discriminant function.- 7.5 Screening a discriminant function.- 7.6 Further uses of the coefficient of determination.- 7.7 Classification of observations.- Discussion.- Further study.- Examples.- 8 Identification analysis.- 8.1 Introduction.- 8.2 Identification analysis as a special case of discriminant analysis.- 8.3 More about standard distance.- 8.4 Identification of a bank note.- 8.5 Analysis of outliers.- Discussion.- Further study.- Examples.- 9 Specification analysis.- 9.1 Standard distance between a sample and a hypothetical mean vector.- 9.2 Specification analysis of the bank notes.- 9.3 Confidence regions for a mean vector.- 9.4 A more general model.- 9.5 Specification faces.- Further study.- Examples.- 10 Principal component analysis.- 10.1 Introduction.- 10.2 Principal components of two variables.- 10.3 Properties of principal components in the multidimensional case.- 10.4 Principal component analysis of the genuine bank notes.- 10.5 The singular case.- 10.6 Principal components, standard distance, and the multivariate normal distribution.- 10.7 Standard errors of the principal component coefficients and related problems.- 10.8 Principal component analysis of several groups.- Discussion.- Further study.- Examples.- 11 Comparing the covariance structures of two groups.- 11.1 Introduction.- 11.2 The bivariate case.- 11.3 The multivariate case.- 11.4 Comparison of the covariance matrices of the genuine and forged bank notes.- 11.5 Partial statistics for the analysis of Ymaxand Ymix.- 11.6 Stepwise analysis of Ymax and Ymix.- 11.7 Relationships to standard distance and principal component analysis.- 11.8 Critical values of the distribution of Fmaxand Fmix.- Discussion.- Further study.- Examples.- 12 Exercises.- 12.1 Exercises based on the bank note data.- 12.2 Additional exercises.- 13 Mathematical appendix.- 13.1 Introduction and preliminaries.- 13.2 Data matrix, mean vector, covariance and correlation.- 13.3 Multiple linear regression.- 13.4 Linear combinations.- 13.5 Multivariate standard distance and the linear discriminant function.- 13.6 Principal component analysis.- 13.7 Comparison of two covariance matrices.- References.
