Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation

发布者：程梦琴发布时间：2019-05-26浏览次数：179

Speaker:Runze Li 教授 Penn State University
Host:Zhao Chen, School of Data Science, Fudan University
Time:10:30-11:30, Jun 5, 2019
Location:Zibin N205, Fudan University
Abstract:In this paper, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the “oracle” method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the desparsified Lasso estimator van de Geer, et al (2014) and the decorrelated score statistic （Ning and Liu, 2017). Simulation studies and real data applications are presented to back up our theoretical findings.
Bio:李润泽是宾州州立大学讲席教授。他的研究方向包括高维数据建模，非参数回归，半参数回归及其统计学的应用。他是IMS，ASA和AAAS fellow. 他曾担任Annals of Statistics的副主编，主编. 现担任Journal of American Statistical Association 的副主编。