Title

On Singular Multivariate Normal Distribution and Its Applications

Publication Type

Journal Article

Publication Date

1996

Abstract

The methods of evaluating the singular multivariate normal distribution have been commonly applied even though the complete analytical proofs are not found. Recently, those evaluation methods are shown to have some errors. In this paper we present a new approach with a complete proof for evaluating the exact two-sided percentage points of a standardized m-variate normal distribution with a singular negative product correlation structure for m = 3 and with a singular negative equi-correlated structure for m [greater-or-equal, slanted] 3. The results are then applied to modify the existing procedures for estimating joint confidence intervals for multinomial proportions and for determining sample sizes. By extending the results from the multivariate normal distribution to the multivariate t-distribution with the corresponding singular correlation structure, we obtain the corrected two-sided exact critical values for the Analysis of Means for m = 4,5.

Discipline

Econometrics

Research Areas

Econometrics

Publication

Computational Statistics and Data Analysis

Volume

22

Issue

3

First Page

271

Last Page

285

ISSN

0167-9473

Identifier

10.1016/0167-9473(95)00050-x

Publisher

Elsevier

Additional URL

http://dx.doi.org/10.1016/0167-9473(95)00050-x

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