Abstract: The statistical inference problem for semiparametric varying coefficient models with fixed effects under missing data is addressed.The varying coefficient functions are handled through local polynomial methods,and fixed effects are eliminated through instrumental variables.The issue of missing data is resolved by employing the Kaplan-Meier product limit estimator,and a semiparametric empirical likelihood ratio statistic is constructed.In appropriate regularity conditions,the proposed estimators are proved to be consistent and asymptotically normal,and the empirical likelihood ratio statistic is shown to follow the standard chi-squared distribution.Monte Carlo simulations reveal that compared with conventional complete-case analysis,the empirical likelihood inference can effectively reduce bias and enhance estimation efficiency.

Key words: semiparametric model, empirical likelihood, fixed effect, missing data