Inference for biased models: A quasi-instrumental variable approach

Lu Lin, Lixing Zhu and Yujie Gai

Journal of Multivariate Analysis, 2016, vol. 145, issue C, 22-36

Abstract: 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 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 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.

Keywords: High-dimensional regression; Non-sparse structure; Instrumental variable; Re-modeling; Bias correction; Dantzig selector (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2015.11.011

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