Exponentially tilted likelihood inference on growing dimensional unconditional moment models

唐年胜，博士，国家杰出青年科学基金获得者，教育部“长江学者”特聘教授，教育部“新世纪优秀人才”，云南省科技领军人才，云南省首批云岭学者，云南省中青年学术和技术带头人，云南省教学名师，云南省学位委员会经济与管理学科评议组成员，博士生导师。云南省高校“统计与信息技术重点实验室”负责人，“云南大学复杂数据统计推断方法研究”省创新团队带头人。

Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted(PET) likelihood for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecification. Under some regularity conditions,we investigate the consistent and oracle properties of the PET estimators of parameters,and show that the constrainedly PET likelihood ratio statistic for testing contrast hypothesis asymptotically follows the chi-squared distribution. Theoretical results reveal that the PET likelihood approach is robust to model misspecification. We study high-order asymptotic properties of the proposed PET estimators.Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.