论文标题
估计信噪比估计的高维随机效应模型的错误指定分析
Misspecification Analysis of High-Dimensional Random Effects Models for Estimation of Signal-to-Noise Ratios
论文作者
论文摘要
高维线性模型中信噪比和残留方差的估计具有各种重要应用，例如生物信息学中的遗传力估计。一种通常称为REML的常用估计量是基于随机效应模型的可能性，在该模型中，回归系数和噪声变量分别假定为I.I.D高斯随机变量。在本文中，我们旨在建立SNR的REML估计器的一致性和渐近分布，当实际系数矢量固定时，并且实际噪声是异质的和相关的，以假设设计矩阵的条目是独立的，并且无独立且无偏度。当噪声是异性但不相关时，也可以一致估计渐近方差。广泛的数值模拟说明了我们的理论发现，也表明我们的理论结果中提出的一些假设可能是可以放松的。
Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications including, e.g. heritability estimation in bioinformatics. One commonly used estimator, usually referred to as REML, is based on the likelihood of the random effects model, in which both the regression coefficients and the noise variables are respectively assumed to be i.i.d Gaussian random variables. In this paper, we aim to establish the consistency and asymptotic distribution of the REML estimator for the SNR, when the actual coefficient vector is fixed, and the actual noise is heteroscedastic and correlated, at the cost of assuming the entries of the design matrix are independent and skew-free. The asymptotic variance can be also consistently estimated when the noise is heteroscedastic but uncorrelated. Extensive numerical simulations illustrate our theoretical findings and also suggest some assumptions imposed in our theoretical results are likely relaxable.
