Fast Rates of Gaussian Empirical Gain Maximization With Heavy-Tailed Noise.

In a regression setup, we study in this brief the performance of Gaussian empirical gain maximization (EGM), which includes a broad variety of well-established robust estimation approaches. In particular, we conduct a refined learning theory analysis for Gaussian EGM, investigate its regression calibration properties, and develop improved convergence rates in the presence of heavy-tailed noise. To achieve these purposes, we first introduce a new weak moment condition that could accommodate the cases where the noise distribution may be heavy-tailed. Based on the moment condition, we then develop a novel comparison theorem that can be used to characterize the regression calibration properties of Gaussian EGM. It also plays an essential role in deriving improved convergence rates. Therefore, the present study broadens our theoretical understanding of Gaussian EGM.

A Powerful Method To Test Associations Between Ordinal Traits and Genotypes.

The methods commonly used to test the associations between ordinal phenotypes and genotypes often treat either the ordinal phenotype or the genotype as continuous variables. To address limitations of these approaches, we propose a model where both the ordinal phenotype and the genotype are viewed as manifestations of an underlying multivariate normal random variable. The proposed method allows modeling the ordinal phenotype, the genotype and covariates jointly. We employ the generalized estimating equation technique and M-estimation theory to estimate the model parameters and deduce the corresponding asymptotic distribution. Numerical simulations and real data applications are also conducted to compare the performance of the proposed method with those of methods based on the logit and probit models. Even though there may be potential limitations in Type I error rate control for our method, the gains in power can prove its practical value in case of exactly ordinal phenotypes.

M-test in linear models with negatively superadditive dependent errors.

This paper is concerned with the testing hypotheses of regression parameters in linear models in which errors are negatively superadditive dependent (NSD). A robust M-test base on M-criterion is proposed. The asymptotic distribution of the test statistic is obtained and the consistent estimates of the redundancy parameters involved in the asymptotic distribution are established. Finally, some Monte Carlo simulations are given to substantiate the stability of the parameter estimates and the power of the test, for various choices of M-methods, explanatory variables and different sample sizes.