In this article, we develop a so‐called profile likelihood ratio test (PLRT) based on the estimated error density for the multiple linear regression model. Unlike the existing likelihood ratio test (LRT), our proposed PLRT does not require any specification on the error distribution. The asymptotic properties are developed and the Wilks phenomenon is studied. Simulation studies are conducted to examine the performance of the PLRT. It is observed that our proposed PLRT generally outperforms the existing LRT, empirical likelihood ratio test and the weighted profile likelihood ratio test in sense that (i) its type I error rates are closer to the prespecified nominal level; (ii) it generally has higher powers; (iii) it performs satisfactorily when moments of the error do not exist (eg, Cauchy distribution); and (iv) it has higher probability of correctly selecting the correct model in the multiple testing problem. A mammalian eye gene expression dataset and a concrete compressive strength dataset are analyzed to illustrate our methodologies.

中文翻译：

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线性回归模型的基于核密度的似然比检验

在本文中，我们基于多元线性回归模型的估计误差密度开发了所谓的轮廓似然比检验（PLRT）。与现有的似然比检验（LRT）不同，我们提出的PLRT不需要任何关于误差分布的规范。开发渐近性质，研究威尔克斯现象。进行模拟研究以检查PLRT的性能。可以看出，在以下方面，我们提出的PLRT通常优于现有的LRT，经验似然比检验和加权轮廓似然比检验：（i）其I型错误率更接近于预定的名义水平；（ii）它通常具有较高的权力；（iii）当错误时刻不存在时（例如柯西分布），其性能令人满意；（iv）在多重测试问题中更有可能正确选择正确的模型。分析了哺乳动物的眼睛基因表达数据集和具体的抗压强度数据集，以说明我们的方法。