Statistical Procedures

From comparative analyses to multiple predictive models

This textbook considers statistical learning applications when interest centers on the conditional distribution of the response variable, given a set of predictors, and when it is important to characterize how the predictors are related to the response.

This book is a self-teaching guide to the SPSS for Windows computer package. 'It is designed to be used hand-in-hand with The New Statistical Analysis of Data by T. W. Anderson and Jeremy D. Finn, although it may be used as a stand-alone manual as well. This guide is very easy to follow since all procedures are outlined in a straightforward, step-by-step format.

The term "robustness" does not lend itself to a clear-cut statistical definition. It seems to have been introduced by G. E. P. Box in 1953 to cover a rather vague concept described in the following way by Kendall and Buckland (1981). Their dictionary states:

In the last few decades the accumulation of large amounts of in­ formation in numerous applications. has stimtllated an increased in­ terest in multivariate analysis. Computer technologies allow one to use multi-dimensional and multi-parametric models successfully. At the same time, an interest arose in statistical analysis with a de­ ficiency of sample data. Nevertheless, it is difficult to describe the recent state of affairs in applied multivariate methods as satisfactory. Unimprovable (dominating) statistical procedures are still unknown except for a few specific cases. The simplest problem of estimat­ ing the mean vector with minimum quadratic risk is unsolved, even for normal distributions. Commonly used standard linear multivari­ ate procedures based on the inversion of sample covariance matrices can lead to unstable results or provide no solution in dependence of data. Programs included in standard statistical packages cannot process 'multi-collinear data' and there are no theoretical recommen­ dations except to ignore a part of the data. The probability of data degeneration increases with the dimension n, and for n > N, where N is the sample size, the sample covariance matrix has no inverse. Thus nearly all conventional linear methods of multivariate statis­ tics prove to be unreliable or even not applicable to high-dimensional data.