Characterizations Of Semi-parametric Partially Linear Regres- Sion Models For Functional Data

In this paper we consider the functional semi-parametric partially linear regres-sion model, using the weighted least squares estimation method and Nadaraya-Waston estimation method, by optimizing each individual, we can obtain the estimations of β and g(z) and some asymptotic results. The Monte-Carlo simulation study is conducted to investigate the finite sample performance of the proposed estimators in the sparse case or the dense case.In addition, we try to extend the empirical likelihood method to the partially linear regression models, get the confidence interval of the non-parametric part, and propose a bias-corrected empirical likelihood that requires neither undersmoothing nor direct bias estimation. Our numerical results demonstrate that the bias-corrected empirical likelihood method produces better confidence regions compared to the normal approx-imation based method.