ABSTRACT Random coefficient regression models are the regression counterparts of the classical random effects models in Analysis of Variance and panel data analysis. While several heuristic methods have been proposed for the detection of such random regression coefficients, little is known on their optimality properties. Based on a nonstandard ULAN property, we are proposing locally asymptotically optimal (in the Hájek-Le Cam sense) parametric, pseudo-Gaussian, and rank-based procedures for this problem. The asymptotic relative efficiencies (with respect to the pseudo-Gaussian procedure) of rank-based tests turn out to be quite high under heavy-tailed and skewed densities, demonstrating the importance of a careful choice of scores. Simulations reveal the excellent finite-sample performances of a class of rank-based procedures based on data-driven scores.

中文翻译：

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随机回归系数的高效伪高斯和基于秩的检测

摘要 随机系数回归模型是方差分析和面板数据分析中经典随机效应模型的回归对应模型。虽然已经提出了几种启发式方法来检测这种随机回归系数，但对其最优性知之甚少。基于非标准的 ULAN 属性，我们针对这个问题提出了局部渐近最优（在 Hájek-Le Cam 意义上）参数化、伪高斯和基于秩的过程。在重尾和偏斜密度下，基于秩的测试的渐近相对效率（相对于伪高斯过程）被证明是相当高的，这表明谨慎选择分数的重要性。