Empirical Likelihood Inference for Partial Functional Linear Model

In this paper, we consider the partial functional linear regression model, and construct the empirical log-likelihood ratio statistic for the unknown regression parameter. It is shown that the proposed statistics have the asymptotic standard chi-square distribution, and hence they can be used to construct the confidence region of the parameter. In addition, the maximum empirical likelihood estimator of the unknown coefficient function is constructed, and its asymptotic behavior is proved. A simulation study and real data analysis are carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities.