Some distribution theory relating to confidence regions in multivariate calibration (Q1110217)

In the problem of multivariate calibration, \textit{E. J. Williams} [Regression analysis. (1959; Zbl 0088.127)] and \textit{J. T. Wood} [to appear in Proc. 11th Internat. Bio. Conf.] have proposed a decomposition of the usual Hotelling's \(T^ 2\) statistic into the sum of two statistics for use in constructing confidence regions. This paper presents general results for the moment terms basic to \textit{Y. Fujikoshi} and \textit{R. Nishii}'s [Hiroshima Math. J. 14, 215-225 (1984; Zbl 0561.62050)] approach to the distributions of these statistics, and presents simple alternative approximations to their percentiles.