Optimal pseudo-Gaussian and rank-based random coefficient detection in multiple regression
Optimal pseudo-Gaussian and rank-based random coefficient detection in multiple regression
复制标题
多元回归中的最优伪高斯和基于排序的随机系数检测
DOI：
10.1214/20-ejs1770
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Mellouk
中科院分区：
文献类型：
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作者：
A. Akharif;M. Fihri;M. Hallin;A. Mellouk
随机系数回归（RCR）模型是方差分析和面板数据分析中随机效应模型的回归版本。随机系数存在的最优检测（等价地，恒定回归系数假设的最优检验）多年来一直是一个开放的问题。最近已经解决了简单回归的情况（Fihri et al.（2017）），这里考虑了多元回归的情况。这个问题提出了几个理论上的挑战：（a）一个非标准的ULAN结构，与对数似然梯度消失在零假设;（B）一个锥形的替代传统的最大极小型最优性概念不再是足够的;（c）一个矩阵的滋扰参数（随机系数的相关结构），没有确定下的零，但有一个非常显着的影响当地的权力。受Novikov（2011）的启发，我们提出了一种新的（局部和渐近）最优性概念，并在给定误差密度下，推导了相应的参数最优方法，并对高斯最优方法进行了适当的修改，证明了其在任意密度和有限阶四阶矩下仍然有效，因此是一种伪高斯检验.然而，这些伪高斯检验的渐近性能，是相当差的偏态和重尾密度。因此，我们还构建了基于等级的测试，可能是基于数据驱动的分数，其渐近相对效率是非常高的伪高斯对应。
Random coefficient regression (RCR) models are the regression versions of random effects models in analysis of variance and panel data analysis. Optimal detection of the presence of random coefficients (equivalently, optimal testing of the hypothesis of constant regression coefficients) has been an open problem for many years. The simple regression case has been solved recently (Fihri et al. (2017)), and the multiple regression case is considered here. This problem poses several theoretical challenges (a)a nonstandard ULAN structure, with log-likelihood gradients vanishing at the null hypothesis; (b) a cone-shaped alternative under which traditional maximin-type optimality concepts are no longer adequate; (c) a matrix of nuisance parameters (the correlation structure of the random coefficients) that are not identified under the null but have a very significant impact on local powers. Inspired by Novikov (2011), we propose a new (local and asymptotic) concept of optimality for this problem, and, for specified error densities, derive the corresponding parametrically optimal procedures.A suitable modification of the Gaussian version of the latter is shown to remain valid under arbitrary densities with finite moments of order four, hence qualifies as a pseudo-Gaussian test. The asymptotic performances of those pseudo-Gaussian tests, however, are rather poor under skewed and heavy-tailed densities. We therefore also construct rank-based tests, possibly based on data-driven scores, the asymptotic relative efficiencies of which are remarkably high with respect to their pseudo-Gaussian counterparts.