Empirical likelihood for high-dimensional partially linear model with martingale difference errors |
| |
Authors: | Guo-Liang Fan Zhi-Qiang Jiang |
| |
Institution: | 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 |
|
|