Rank Transformation as a Method of Discrimination with Some Examples.

摘要

The procedure of statistical discrimination is simple in theory but not so simple in practice. An observation x/sub approx.O/,possible multivariate,is to be classified into one of several populations pi sub 1 ,...,pi /sub k/,which have,respectively,the density functions f sub 1 (x),...,f/sub k/(x). The decision procedure is to evaluate each density function at X/sub O/,to see which function gives the largest value f/sub i/(x/sub approx.O),and then to declare that x/sub approx.O/belongs to the population corresponding to the largest value. If these densities can be assumed to be normal with equal covariance matrices,then the decision procedure is known as Fisher's linear discriminant function (LDF) method. In the case of unequal covariance matrices,the procedure is called the quadratic discriminant function (QDF) method. If the densities cannot be assumed to be normal,then the LDF and QDF might not perform well. Several different procedures have appeared in the literature which offer discriminant procedures for nonnormal data;however,these procedures are generally difficult to use and are not readily available as canned statistical programs. Another approach to discriminant analysis is to use some sort of mathematical transformation on the samples so that their distribution function is approximately normal,and then use the convenient LDF and QDF methods. One transformation that applies to all distributions equally well is the rank transformation. The result of this transformation is that a very simple and easy-to-use procedure is made available. This procedure is quite robust,as is evidenced by comparisons of the rank transform results with several published simulation studies. 32figures, 15tables. (ERA citation 04:038029)