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Likelihood-based inference in censored exponential regression models

机译：审查指数回归模型中的基于可能性的推断

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This paper deals with the issue of testing hypotheses in the censored exponential regression model in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic under a null hypothesis and the corresponding reference chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in the class of censored exponential regression models. A Bartlett-type correction for the gradient test is derived in this paper in this class of models. Additionally, we also propose bootstrap-based inferential improvements to the four tests mentioned. We numerically compare the tests through extensive Monte Carlo simulation experiments. The numerical results reveal that the corrected and bootstrapped tests exhibit type I error probability closer to the chosen nominal level with virtually no power loss. We also present an empirical application for illustrative purposes.
机译：本文涉及在小型和中等大小样本中被审判指数回归模型中的测试假设问题。我们专注于四次测试，即沃尔德，似然比，分数和渐变测试。这些测试依赖于渐近结果，并且当样本大小足够大时不可靠，以保证在零假设下测试统计的精确分布与相应的参考Chi平方渐近分布之间的良好一致性。 Bartlett和Bartlett型更正通常衰减测试的尺寸失真。这些校正在文献中可用，以获得审查指数回归模型类中的似然比和分数测试。在这篇论文中，在这篇型号中推出了梯度测试的Bartlett型校正。此外，我们还提出了基于引导的推理改进，以提及的四个测试。我们通过广泛的Monte Carlo仿真实验进行了数字地比较了测试。数值结果表明，校正和自动启动的测试表现出I型错误概率与所选标称级别更接近所选择的标称级别，几乎没有功率损耗。我们还出现了用于说明目的的实证申请。

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