主題: Robust-BD Estimation and Inference for Varying-Dimensional General Linear Models
主講人:張春明教授(美國(guó)威斯康辛大學(xué)統(tǒng)計(jì)系教授)
時(shí)間:2015年6月29日(周一)下午15:00-16:00
地點(diǎn):北院卓遠(yuǎn)樓305
主辦單位:統(tǒng)計(jì)與數(shù)學(xué)學(xué)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.
張春明教授簡(jiǎn)介:統(tǒng)計(jì)學(xué)博士,,美國(guó)威斯康星大學(xué)麥迪遜分校統(tǒng)計(jì)系教授,,研究領(lǐng)域包括半?yún)?shù)/非參數(shù)統(tǒng)計(jì)推斷、多重檢驗(yàn)、統(tǒng)計(jì)理論與方法在神經(jīng)信息學(xué)和生物信息學(xué)中的應(yīng)用等。曾任/擔(dān)任Annals of Statistics、Journal of the American Statistical Association, Journal of Statistical Planning and Inference等多個(gè)國(guó)際統(tǒng)計(jì)學(xué)SCI期刊副主編,。