Penalized empirical likelihood for high-dimensional partially linear errors-in-function model with martingale difference errors. Issue 6 (1st November 2020)

• Record Type: Journal Article
• Authors: Bang-Qiang, HE; Sheng-Ri, LV
• Is Part Of: Statistics. Volume 54:Issue 6(2020)
• Page Start: 1214
• Page End: 1231
• Publication Date: 2020-11-01
• Subjects: Penalized empirical likelihood -- partially linear model -- errors-in-function -- martingale difference sequence; 62G15 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1835908
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: For the high-dimensional partially linear errors-in-function model with martingale difference errors, we, in this paper, propose an empirical log-likelihood ratio function for the regression parameter. The empirical log-likelihood ratio is proven to be asymptotically chi-squared. In addition, we propose penalized empirical likelihood (PEL) for the parameter. By using an appropriate penalty function, we show that PEL has the oracle property. Also, we obtain the PEL ratio is defined and its limiting distribution is asymptotically chi-squared under the null hypothesis. Moreover, simulation studies and a real data example are undertaken to assess the finite sample performance of our proposed method.