The Influence of Assumptions Implicit in a Model on Parametric Inference
| Autor: | J. B. F. Field, A. T. James, W. N. Venables |
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| Rok vydání: | 1989 |
| Předmět: | |
| Zdroj: | Journal of the American Statistical Association. 84:101-106 |
| ISSN: | 1537-274X 0162-1459 |
| DOI: | 10.1080/01621459.1989.10478743 |
| Popis: | In choosing a model, there are important considerations beyond the goodness of fit, namely that the subsequent inferences should not rely on questionable assumptions implicit in the model, because otherwise they will be suspect. The two-parameter lognormal distribution provides an example. The symmetry on the log scale leads to the anomaly that relative frequencies of classes in the lower tail can substantially affect inferences on the upper tail. This is contrary to the realities of the alcohol consumption example considered in this article, as well as other practical situations. A mathematical analysis of assumptions is made, using the fact that maximum likelihood estimation is asymptotically equivalent to least squares regression. It is shown that, for inferences regarding the upper tail of the two-parameter lognormal distribution, the introduction of the usual third parameter, or, almost equivalently, censoring the lower tail, can remove the anomaly. The theoretical results are illustrated by... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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