An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials

Traditional discussions of goodness-of-fit tests for multinomial data consider asymptotic chi-squared properties under the assumption that all expected cell frequencies become large. This condition is not always satisfied, however, and another asymptotic theory must be considered. For testing a spec...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1980-06, Vol.75 (370), p.336-344
Main Authors: Koehler, Kenneth J., Larntz, Kinley
Format: Article
Language:English
Subjects:
Approximation
Asymptotic approximations
Chi-squared
Degrees of freedom
Gaussian distributions
Likelihood ratio statistic
Mathematical moments
Null hypothesis
Pearson statistic
Probabilities
Ratio test
Sample size
Statistical variance
Statistics
Theory and Methods
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Summary:Traditional discussions of goodness-of-fit tests for multinomial data consider asymptotic chi-squared properties under the assumption that all expected cell frequencies become large. This condition is not always satisfied, however, and another asymptotic theory must be considered. For testing a specified simple hypothesis, Morris (1975) and Hoist (1972) gave conditions for the asymptotic normality of the Pearson and likelihood ratio statistics when both the sample size and number of cells become large (even if the expected cell frequencies remain small). Monte Carlo techniques are used to examine the applicability of the normal approximations for moderate sample sizes with moderate numbers of cells.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1980.10477473