Empirical Likelihood for Partially Linear Models

• Published in: Journal of multivariate analysis Vol. 72; no. 1; pp. 132 - 148
• Main Authors: Shi, Jian, Lau, Tai-Shing
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.01.2000; Elsevier
• Series: Journal of Multivariate Analysis
• Subjects: empirical likelihood; Exact sciences and technology; Linear inference, regression; Mathematics; Nonparametric inference; nonparametric likelihood ratio; partially linear model; partially linear model, empirical likelihood, nonparametric likelihood ratio, sieve approximation, weight functions; Probability and statistics; Sciences and techniques of general use; sieve approximation; Statistics; weight functions; partially linear model, empirical likelihood, nonparametric likelihood ratio, sieve approximation, weight functions; Lagrange multiplier; Weight function; Sieve approximation; Law of large numbers; Likelihood ratio; Non parametric estimation; Empirical likelihood; Maximum likelihood; Partially linear model; Chi square; Linear model
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1006/jmva.1999.1866

In this paper, we consider the application of the empirical likelihood method to partially linear model. Unlike the usual cases, we first propose an approximation to the residual of the model to deal with the nonparametric part so that Owen's (1990) empirical likelihood approach can be applied. Then, under quite general conditions, we prove that the empirical log-likelihood ratio statistic is asymptotically chi-squared distributed. Therefore, the empirical likelihood confidence regions can be constructed accordingly.