JSM 2004 - Toronto

Abstract #301528

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Activity Number: 233
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
Sponsor: General Methodology
Abstract - #301528
Title: New Tables of the Largest Root of a Matrix in Mulivariate Analysis
Author(s): William W.S. Chen*+
Companies: Internal Revenue Service
Address: Statistics of Income, Washington, DC, 20013,
Keywords: characteristic roots ; extended tables ; Fisher-Girshick-Shu-Roy ; distribution ; percentage points
Abstract:

The Fisher-Girshick-Shu-Roy distribution (1939), which has interested statisticians more than six decades, is revisited. Instead of using Pillai's K.C.S. method by neglecting higher-order terms of the cumulative distribution function (c.d.f.) of the largest root to approximate the percentage points, we simply keep the whole c.d.f. and apply its natural nondecreasing property to calculate the exact probabilities. We forcus on distribution when there are seven or eight characteristic roots. At the duplicated percentage points we found our computed percentage points consistent to the existing tables. Our tabulations, however, have greatly extended those tables.

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