ABSTRACT Maji et al. [Robust statistical inference based on the C-divergence family. Ann Inst Stat Math. 2019;71:1289–1322] introduced the minimum C-divergence estimators and plugging them in the C-divergence measures give test statistics for testing simple null and composite null hypotheses. One inconvenience of these test statistics is that their asymptotic distribution is not, in general, a chi-square distribution but a linear combination of chi-square distributions. To overcome this inconvenience, in this paper we consider Wald-type test statistics based on minimum C-divergence estimators. We establish that this family of test statistics is a chi-square distribution and we get an approximation of the power function under simple null hypothesis and composite null hypothesis. We have calculated both first order and second order influence function of the Wald-type test statistics and based on it we can see the robustness of the family of test statistics considered in this paper. Both simulated and real data examples have been shown as part of numerical results.

中文翻译：

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基于最小 C 散度估计量的鲁棒 Wald 型检验统计量

摘要 Maji 等人。[基于C-divergence族的稳健统计推断。Ann Inst 统计数学。2019;71:1289-1322] 介绍了最小 C 散度估计量，并将它们插入 C 散度度量中，从而提供测试统计数据以测试简单的零假设和复合零假设。这些检验统计量的一个不便之处在于它们的渐近分布通常不是卡方分布，而是卡方分布的线性组合。为了克服这种不便，在本文中，我们考虑了基于最小 C 散度估计量的 Wald 型检验统计量。我们确定这组检验统计量是卡方分布，我们得到了简单原假设和复合原假设下的幂函数的近似值。我们已经计算了 Wald 型检验统计量的一阶和二阶影响函数，并在此基础上我们可以看到本文考虑的检验统计量族的稳健性。模拟和真实数据示例均已显示为数值结果的一部分。