统计与管理学院2017年学术报告第32期

【主  题】Variable Selection for Partially Linear Models via Partial Correlatio

【报告人】刘婧媛, 教授

厦门大学经济学院统计系、王亚南经济研究院

【时  间】 2017年05月19日（星期五）16:00－17:00

【地  点】 上海财经大学统计与管理学院大楼1208室

【摘  要】Partially linear models (PLM) are among the most popular and useful semiparametric extensions to linear models, and have been widely used in research areas like economics and finance. The variable selection issues of these models, especially in the ultrahigh dimensional settings, yet are not discussed to a large extent in literature. Several penalized regression techniques were generalized from linear models to PLM. Most of them, however, are still limited to low dimensionality, hence are not statistically feasible, or suffer from computational inefficiency for high dimensional data. In this paper, we propose a new variable selection scheme for PLM with ultrahigh dimensional covariates from a different starting point - the partial correlation learning. We discuss the partial faithfulness proposed by Buhlmann et al. 2010 under the ultrahigh dimensional PLM setting, and propose a variable selection method via evaluating the partial correlations between the partial residuals of the response and that of the predictors. Unlike Buhlmann et al. 2010, normality is not required for the theoretical properties of the procedure, and ultrahigh dimensionality is allowed by our method. The model selection consistency is carefully studied, both theoretically and empirically, and the root- n consistency and asymptotic normality of the parameter estimations are also discussed. To enhance the finite sample performance, we further incorporate the extended BIC for tuning the partial correlation cutoff value. The usage of the proposed method is demonstrated by two real data analyses - the Istanbul stock exchange data and the supermarket data.

【邀请人】 冯兴东