The Conditional Distribution of Goodness-of-Fit Statistics for Discrete Data
作者:
Peter McCullagh,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1986)
卷期:
Volume 81,
issue 393
页码: 104-107
ISSN:0162-1459
年代: 1986
DOI:10.1080/01621459.1986.10478244
出版商: Taylor & Francis Group
关键词: Conditional inference;Cumulants;Edgeworth approximation;Log-linear model;Linear logistic model;Sparse data
数据来源: Taylor
摘要:
I consider the distribution of Pearson's statistic and of the likelihood-ratio goodness-of-fit statistic for discrete data in the important case where the data are extensive but sparse. It is argued that the appropriate reference distribution is conditional on the sufficient statistic for the unknown regression parameters, β. The first three conditional asymptotic cumulants are derived by Edgeworth expansion, and these are used for the computation of tail probabilities. The principal advantage of the limit considered here, as opposed to the more usualX2limit, is that the cell counts need not be large.
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