Random Variable Techniques

Abstract

In some parts of statistical inference it is customary to speak entirely in random variable terms, as in the analysis of variance. One considers his job finished when he writes the ratio of two independently distributed chi-square random variables, the denominator a central chi-square. There are a number of distribution problems in which by manipulation of the random variables involved one reduces the distribution problem to determination of the distribution of a relatively simple function of several independently distributed random variables. The theory of best linear unbiased estimation whereby a noncentral chi-square is obtained that is distributed independently of the sum of squares of error is in the meaning of this chapter a theory using random variable techniques. Another example that can at least partially be treated using random variable techniques is the example of Section 10.3, the multivariate beta density functions. See also Remark 5.7.3.