An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials
Kenneth J. KoehlerDepartment of Statistics , Iowa State University , Ames , IA , 50010 , USAKinley LarntzSchool of Statistics, University of Minnesota , St. Paul , MN , 55108 , USA
1980en
ABI
Abstract
Abstract 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.
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