Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10525125 | Journal of Statistical Planning and Inference | 2011 | 11 Pages |
Abstract
In this paper, we study a working sub-model of partially linear model determined by variable selection. Such a sub-model is more feasible and practical in application, but usually biased. As a result, the common parameter estimators are inconsistent and the corresponding confidence regions are invalid. To deal with the problems relating to the model bias, a nonparametric adjustment procedure is provided to construct a partially unbiased sub-model. It is proved that both the adjusted restricted-model estimator and the adjusted preliminary test estimator are partially consistent, which means when the samples drop into some given subspaces, the estimators are consistent. Luckily, such subspaces are large enough in a certain sense and thus such a partial consistency is close to global consistency. Furthermore, we build a valid confidence region for parameters in the sub-model by the corresponding empirical likelihood.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yujie Gai, Lu Lin, Xiuli Wang,