The Number of Classes in Chi-Squared Goodness-of-Fit Tests
| Autor: | W. C. M. Kallenberg, B. F. Schriever, J. Oosterhoff |
|---|---|
| Rok vydání: | 1985 |
| Předmět: |
Statistics and Probability
media_common.quotation_subject Null (mathematics) Asymptotic theory (statistics) Infinity Asymptotically optimal algorithm Goodness of fit Sample size determination Simple (abstract algebra) Likelihood-ratio test Statistics Statistics Probability and Uncertainty Mathematics media_common |
| Zdroj: | Journal of the American Statistical Association. 80:959-968 |
| ISSN: | 1537-274X 0162-1459 |
| DOI: | 10.1080/01621459.1985.10478211 |
| Popis: | The power of Pearson chi-squared and likelihood ratio goodness-of-fit tests based on different partitions is studied by considering families of densities “between” the null density and fixed alternative densities. For sample sizes n → ∞, local asymptotic theory with respect to the number of classes k is developed for such families. Simple sufficient and almost necessary conditions are derived under which it is asymptotically optimal to let k tend to infinity with n. A numerical study shows that the results of the asymptotic local theory for contamination families agree well with the actual power performance of the tests. For heavy-tailed alternatives, the tests have the best power when k is relatively large. Unbalanced partitions with some small classes in the tails perform surprisingly well, in particular when the alternatives have fairly heavy tails. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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