The likelihood ratio, Wald, score and gradient test statistics can result in misleading conclusions when the assumed parametric model to the data at hand is not correctly specified. To overcome this issue, robust versions of these test statistics have been proposed in the statistic literature under model misspecification. In this paper, we address the issue of performing hypothesis testing inference in location-scale models under model misspecification. Monte Carlo simulation experiments are carried out to verify the performance of the robust test statistics, as well as usual test statistics (i.e. non-robust), in the class of location-scale models under model misspecification. The simulation results reveal that the robust tests we propose are more reliable than the usual tests since they lead to an accurate inference. An empirical application to real data is considered for illustrative purposes.

中文翻译：

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模型错误指定下位置尺度模型中的假设检验推理

当针对手头数据的假设参数模型没有正确指定时，似然比、Wald、分数和梯度检验统计量可能会导致误导性结论。为了克服这个问题，在模型错误指定的统计文献中已经提出了这些测试统计量的稳健版本。在本文中，我们解决了在模型错误指定下在位置尺度模型中执行假设检验推理的问题。进行蒙特卡罗模拟实验以验证鲁棒测试统计以及通常的测试统计（即非鲁棒）在模型错误指定下的位置尺度模型类中的性能。模拟结果表明，我们提出的鲁棒测试比通常的测试更可靠，因为它们会导致准确的推断。