Properties of simultaneous confidence intervals for multinomial proportions |
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Authors: | Warren L. May William D Johnson |
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Affiliation: | 1. department of Preventive Medicine , The University of Mississippi Medical Center , Jackson, Mississippi, 39216-45052500 North State Street;2. department of Biometry and Genetics , Louisiana State University Medical Center , New Orleans, Louisiana, 70112-13931901 Perdido Street |
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Abstract: | Inversion of Pearson's chi-square statistic yields a confidence ellipsoid that can be used for simultaneous inference concerning multinomial proportions. Because the ellipsoid is difficult to interpret, methods of simultaneous confidence interval construction have been proposed by Quesenberry and hurst,goodman,fitzpatrick and scott and sison and glaz . Based on simulation results, we discuss the performance of these methods in terms of empirical coverage probabilities and enclosed volume. None of the methods is uniformly better than all others, but the Goodman intervals control the empirical coverage probability with smaller volume than other methods when the sample size supports the large sample theory. If the expected cell counts are small and nearly equal across cells, we recommend the sison and glaz intervals. |
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Keywords: | categorical data multinomial distribution simultaneous interval estimation accuracy of confidence statement |
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