Inference for biased models: A quasi-instrumental variable approach

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• 作者：Lu Lin^a ; ^b ; ¹ ; Lixing Zhu^c ; ^d ; ¹ ; ^{lzhu@hkbu.edu.hk" class="auth_mail" title="E-mail the corresponding author} ; Yujie Gai^e
• 关键词：62C05 ; 62F10 ; 62F12 ; 62G05
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：145
• 期：Complete
• 页码：22-36
• 全文大小：428 K

文摘

For linear regression models who are not exactly sparse in the sense that the coefficients of the insignificant variables are not exactly zero, the working models obtained by a variable selection are often biased. Even in sparse cases, after a variable selection, when some significant variables are missing, the working models are biased as well. Thus, under such situations, root-n$n$ consistent estimation and accurate prediction could not be expected. In this paper, a novel remodeling method is proposed to produce an unbiased model when quasi-instrumental variables are introduced. The root-n$n$ estimation consistency and the asymptotic normality can be achieved, and the prediction accuracy can be promoted as well. The performance of the new method is examined through simulation studies.