Abstract
Three problems in multivariate analysis are considered. Exact, approximate, and numerical solutions are given in various instances. First, the exact upper percentage points are given for the sample distribution of the studentized bivariate range for small samples, and Monte Carlo studies are used to assess the power of the test for detecting outliers using conservative percentage points which are given for moderate sized samples. The maximum value of the second largest studentized distance (the studentized range being the largest studentized distance) in a sample of size n from a p-variate normal population is derived. It is [equation in PDF]. Second, a maximum likelihood test of the hypothesis of the equality of the variance-covariance matrices of two normally distributed correlated vectors x and y is given for the case when the matrix Cov(x, y) is symmetric. By using Roy's union-intersection principle as well as the likelihood ratio criterion, approximate and numerical solutions are given as estimators for use in the test statistics for the above hypothesis when the matrix Cov(x, y) is not symmetric. Third, several methods are investigated empirically for the optimal selection of groups of variables by considering only the sample regression coefficients (or statistics derived from them) of the independent variables when the dependent variable is regressed on all of them together. This includes selection of groups of variables in discriminant analysis also.
Smith, Patricia Lee Murphree (1975). Some problems in multivariate analysis. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -184571.