β Scribed by D. Morales; L. Pardo; I. Vajda
No coin nor oath required. For personal study only.
The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by _-finite measures and parametrized by vector-valued variables. It introduces ,-divergence testing statistics as alternatives to the classical ones: the generalized likelihood ratio and the statistics of Wald and Rao. It is shown that, under the assumptions of standard type about hypotheses and model densities, the results about asymptotic distribution of the classical statistics established so far for the counting and Lebesgue dominating measures (discrete and continuous models) remain true also in the general case. Further, these results are extended to the ,-divergence statistics with smooth convex functions ,. The choice of ,-divergence statistics optimal from the point of view of power is discussed and illustrated by several examples.
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Critical values of the test statistic proposed by Al-Shiha and Yang (1999) for analyzing unreplicated factorials are estimated by fitting an appropriate linear model. Some important properties of the test are also provided.
## Suvmary This paper is concerned with the power behaviour of four goodness-of-fit test statistics in sparse multinomials with k cells. Most previous work has been concerned only with both Pearson's Xz and the likelihood ratio test statistics. We consider in this study, two additional test statis