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Empirical likelihood for high-dimensional partially linear model with martingale difference errors
Authors:Guo-Liang Fan  Zhi-Qiang Jiang
Affiliation:1. Institute of Statistics and Big Data, Renmin University of China, Beijing, China;2. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China;3. School of Mathematics &4. Physics, Anhui Polytechnic University, Wuhu, China
Abstract:In this paper, we focus on the empirical likelihood (EL) inference for high-dimensional partially linear model with martingale difference errors. An empirical log-likelihood ratio statistic of unknown parameter is constructed and is shown to have asymptotically normality distribution under some suitable conditions. This result is different from those derived before. Furthermore, an empirical log-likelihood ratio for a linear combination of unknown parameter is also proposed and its asymptotic distribution is chi-squared. Based on these results, the confidence regions both for unknown parameter and a linear combination of parameter can be obtained. A simulation study is carried out to show that our proposed approach performs better than normal approximation-based method.
Keywords:Confidence region  empirical likelihood  high-dimensional data  martingale difference  partially linear model
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