Penalized empirical likelihood for partially linear errors-in-variables models

Xia Chen () and Liyue Mao
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Xia Chen: Shaanxi Normal University
Liyue Mao: Shaanxi Normal University

AStA Advances in Statistical Analysis, 2020, vol. 104, issue 4, No 3, 597-623

Abstract: Abstract In this paper, we study penalized empirical likelihood for parameter estimation and variable selection in partially linear models with measurement errors in possibly all the variables. By using adaptive Lasso penalty function, we show that penalized empirical likelihood has the oracle property. That is, with probability tending to one, penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. Also, we introduce the penalized empirical likelihood ratio statistic to test a linear hypothesis of the parameter and prove that it follows an asymptotic Chi-square distribution under the null hypothesis. Some simulations and an application are given to illustrate the performance of the proposed method.

Keywords: Penalized empirical likelihood; Measurement error; Variable selection; Partially linear models; 62F12; 62G05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10182-020-00365-6

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