Empirical Likelihood For Semiparametric Errors-in-variables Models

In this article,block empirical likelihood inference for semiparametric varying-coefficient partially linear errors-in-variables models and partially linear errors-in-variables models with longitudinal data are investigated respectively. We apply the block empirical likelihood procedure to accommodate the within-group correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric components, which are of primary interest, is suggested. And the non-parametric version of the Wilk’s theorem is derived under mild conditions. Thus, the empirical likelihood confidence region with asymptotically correct coverage proba-bilities for parametric components can be constructed.That above models were discussed when errors are assumed to be indepen-dent and identically distributed random variables. However, in many cases, the homoscedastic assumption for the errors is strong. Heteroscedasticity is often found in residuals form both cross-sectional and time series modeling in applications. As we all known, the ordinary least squares estimator become inconsistent when the errors are heteroscedastic.Take those issues into consideration,the another purpose of this article to use the empirical likelihood method to study the confidence regions construction for the parameters of interest in a semiparametric varying coefficient heteroscedastic par-tially linear EV models and partially linear errors-in-variables models respectively. When errors variances is known and unknown cases, the two different empirical log-likelihood ratio for the parametric components were proposed and nonparametric version of Wilks’theorem were derived, respectively. Simulation study shows that the empirical likelihood approach has a nice properties.