ABSTRACT In the present work, we consider parameter estimation and hypothesis testing based on a general class of measures, namely the -power divergence family for multinomial populations. In particular, we propose a general family of double index -test statistics that involves two indices, the values of which play a key role in the effectiveness and accuracy of the proposed methodology. The asymptotic properties of the associated estimators are examined together with the power of the test and the asymptotic distribution under the contiguous alternatives. Finally, we explore through extensive simulations, the effect of the shape of the multinomial distribution on the performance of the proposed test.

中文翻译：

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基于检验统计量的双指标族的多项总体的统计推断

摘要 在目前的工作中，我们考虑了基于一般度量类别的参数估计和假设检验，即多项式总体的幂散度族。特别是，我们提出了一个一般的双指数检验统计系列，它涉及两个指数，其值在所提出的方法的有效性和准确性中起着关键作用。相关估计量的渐近特性与检验的功效和连续备选下的渐近分布一起检查。最后，我们通过广泛的模拟探索多项分布的形状对建议测试性能的影响。