主题： Robust-BD Estimation and Inference for Varying-Dimensional General Linear Models

主讲人：张春明教授（美国威斯康辛大学统计系教授）

时间：2015年6月29日（周一）下午15:00-16:00

地点：北院卓远楼305

主办单位：统计与数学学院

摘要：This paper investigates new aspects of robust inference for general linear models, calling for a broader array of error measures, beyond the conventional notion of quasi-likelihood, and allowing for a diverging number of parameters. We propose a class of robust error measures, called robust-BD, based on the notion of Bregman divergence (BD). That includes the (negative) quasi-likelihood and many other commonly used error measures as special cases, and we introduce the robust-BD estimators of parameters. We re-examine the classical likelihood ratio-type test statistic, constructed by replacing the negative log-likelihood with the robust-BD, and find that its asymptotic null distribution is a sum of weighted chi-square with weights relying on unknown quantities, thus is not asymptotically distribution free. We propose a robust version of the Wald-type test statistic, based on the robust-BD estimator, and show that it is asymptotically chi-square (central) under the null, thus distribution free, and chi-square (noncentral) under the contiguous alternatives. Numerical examples are presented to illustrate the computational simplicity and effectiveness of the proposed estimator and test in the presence of outliers.

张春明教授简介：统计学博士，美国威斯康星大学麦迪逊分校统计系教授，研究领域包括半参数/非参数统计推断、多重检验、统计理论与方法在神经信息学和生物信息学中的应用等。曾任/担任Annals of Statistics、Journal of the American Statistical Association, Journal of Statistical Planning and Inference等多个国际统计学SCI期刊副主编。