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Title: On singular multivariate normal distribution and its applications
Authors: Kwong, K.-S. 
Iglewicz, B.
Keywords: Analysis of Means
Confidence intervals
Multinomial distribution
Sample size estimation
Issue Date: 1996
Source: Kwong, K.-S., Iglewicz, B. (1996). On singular multivariate normal distribution and its applications. Computational Statistics and Data Analysis 22 (3) : 271-285. ScholarBank@NUS Repository.
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 ≥ 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.
Source Title: Computational Statistics and Data Analysis
ISSN: 01679473
DOI: 10.1016/0167-9473(95)00050-X
Appears in Collections:Staff Publications

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