Ensemble estimation and variable selection with semiparametric regression models

Author:

Shin Sunyoung1,Liu Yufeng2,Cole Stephen R3,Fine Jason P4

Affiliation:

1. Department of Mathematical Sciences, University of Texas at Dallas, 800 W. Campbell Rd., Richardson, Texas 75080, U.S.A. sunyoung.shin@utdallas.edu

2. Department of Statistics and Operations Research, CB# 3260, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. yfliu@email.unc.edu

3. Department of Epidemiology, CB# 7435, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. cole@unc.edu

4. Department of Biostatistics, CB# 7420, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. jfine@email.unc.edu

Abstract

Summary We consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components, with an efficient estimator of the regression parameter available for each component. An optimal weighted combination of the component estimators, named an ensemble estimator, may be employed as an overall estimate of the regression parameter, and may be fully efficient under uncorrelatedness conditions. This approach is useful when the full likelihood function may be difficult to maximize, but the components are easy to maximize. It covers settings where the nuisance parameter may be estimated at different rates in the component likelihoods. As a motivating example we consider proportional hazards regression with prospective doubly censored data, in which the likelihood factors into a current status data likelihood and a left-truncated right-censored data likelihood. Variable selection is important in such regression modelling, but the applicability of existing techniques is unclear in the ensemble approach. We propose ensemble variable selection using the least squares approximation technique on the unpenalized ensemble estimator, followed by ensemble re-estimation under the selected model. The resulting estimator has the oracle property such that the set of nonzero parameters is successfully recovered and the semiparametric efficiency bound is achieved for this parameter set. Simulations show that the proposed method performs well relative to alternative approaches. Analysis of an AIDS cohort study illustrates the practical utility of the method.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Iteratively Reweighted Group Lasso Based on Log-Composite Regularization;SIAM Journal on Scientific Computing;2021-01

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