Statistical inference for high-dimensional models via recursive online-score estimation

Chengchun Shi, Rui Song, Wenbin Lu and Runzi Li

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: In this article, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the “oracle” method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the desparsified Lasso estimator and the decorrelated score statistic. Simulation studies and real data applications are presented to back up our theoretical findings. Supplementary materials for this article are available online.

Keywords: confidence interval; Ultrahigh dimensions; Generalized linear models; online estimations; Online estimation; Confidence interval (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2020-01-23
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Journal of the American Statistical Association, 23, January, 2020. ISSN: 0162-1459

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:103043

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