Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (6): 1019-1031.

• Articles •     Next Articles

Multi-Step-Adjustment Consistent Inference for Biased Sub-Model of Multidimensional Linear Regression

 ZENG Yun-Hui1,2, LIN Lu1, WANG Xiu-Li1,3   

  1. 1.School of Mathematical Science, Shandong University, Jinan 250100|2.Shandong Computer Science Center, Jinan 250014;
    3.School of Mathematical Science, Shandong Normal University, Jinan 250014
  • Received:2011-11-25 Revised:2012-10-12 Online:2012-12-25 Published:2012-12-25
  • Supported by:

    国家自然科学基金(10921101, 11171188)和山东省自然科学基金(ZR2010AZ001, ZR2011AQ007)资助

Abstract:

When the dimension of covariate is high, one usually uses a sub-model as working model. Such a model may be biased because not all relevant variables are contained in it. Thus the resulting estimator of parameter in the sub-model may be inconsistent. In this paper, we shall construct a conditionally unbiased model by multi-step-adjustment. Compared with the existing methods, the adjusted model only adopts univariate nonparametric estimations. A globally consistent estimator of parameter in the sub-model is constructed, and its asymptotic normality is also obtained. The simulation results further illustrate that the performance of the estimator based on the adjusted model is better than those of the estimators derived from the sub-model and the full model.

Key words: Linear regression, Biased sub-model, Consistent estimation, Principal component regression, Independent component analysis

CLC Number: 

  • 62F10
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