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The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "For both applied and theoretical statisticians as well as investigators working in the many areas in which relevant use can be made of discriminant techniques, this monograph provides a modern, comprehensive, and systematic account of discriminant analysis, with the focus on the more recent advances in the field." –SciTech Book News ". . . a very useful source of information for any researcher working in discriminant analysis and pattern recognition." –Computational Statistics Discriminant Analysis and Statistical Pattern Recognition provides a systematic account of the subject. While the focus is on practical considerations, both theoretical and practical issues are explored. Among the advances covered are regularized discriminant analysis and bootstrap-based assessment of the performance of a sample-based discriminant rule, and extensions of discriminant analysis motivated by problems in statistical image analysis. The accompanying bibliography contains over 1,200 references.
The present paper demonstrates how Structural Equation Modelling (SEM) can be used to formulate a test of the difference in means between groups on a number of dependent variables. A Monte Carlo study compared the Type I error rates of the Likelihood Ratio (LR) Chi-square ($\chi\sp2$) statistic (SEM test criterion) and Hotelling's two-sample T$\sp2$ statistic (MANOVA test criterion) in detecting differences in means between two independent samples. Seventy-two conditions pertaining to average sample size ((n$\sb1$ + n$\sb2$)/2), extent of inequality of sample sizes (n$\sb1$:n$\sb2$), number of variables (p), and degree of inequality of variance-covariance matrices ($\Sigma\sb1$:$\Sigma\sb2$) were modelled. Empirical sampling distributions of the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic consisted fo 2000 samples drawn from multivariate normal parent populations. The actual proportion of values that exceeded the nominal levels are presented. The results indicated that, in terms of maintaining Type I error rates that were close to the nominal levels, the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic were comparable when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was relatively large (i.e., 30:1). However, when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was small (i.e., 10:1) Hotelling's T$\sp2$ statistic was preferred. When $\Sigma\sb{1} \not=\Sigma\sb2$ the LR $\chi\sp2$ statistic provided more appropriate Type I error rates under all of the simulated conditions. The results are related to earlier findings, and implications for the appropriate use of the SEM method of testing for group mean differences are noted.
Emphasizes the role of statistics and mathematics in the biological sciences.
Reflecting also the increasingly image-based nature of data, especially in remote sensing, the book outlines extensions of discriminant analysis motivated by problems in statistical image analysis." "The sequence of chapters is clearly and logically developed, beginning with a general introduction to discriminant analysis in Chapter 1.