Statistical Inference For Heteroscedastic Semi-Parametric Varying Coefficient EV Models

Semi-parametric varying coefficient models combine the advantages of partial linear regres-sion models and varying coefficient models, and they can better fit the actual data. It is a hot research direction in statistical field in recent years. Sometimes measurement error data and heteroscedastic data can be arised in practical application. Therefore, statistical inference of semi-parametric varying coefficient models is significant both in theory and in practice under heteroscedasticity and the error of measurement data.The research work of this paper mainly includes the following two aspects:1. For the heteroscedastic semi-parametric varying coefficient models with measuremen-t error of associated explanatory variables of the parametric component, and the problem of estimating parametric and nonparametric components in this model are studied. Initial esti-mates for the regression and varying coefficients are first constructed by the modified profile least squares procedure without input from heteroscedasticity, a bias-corrected kernel estimate for the variance function then is proposed, which in turn is used to define re-weighted estimates of the regression and varying coefficients of the heteroscedastic semi-parametric varying coef-ficient error-in-variables (EV) models. Large sample properties of the proposed estimates are thoroughly investigated under some regular conditions. The finite sample performance of the proposed estimates are assessed by an extensive simulation study. The simulation results show that the re-weighted estimates outperform the initial estimates and the naive estimates.2. For the heteroscedastic semi-parametric varying coefficient EV models under restricted condition, and the estimation and testing problems are investigated. The re-weighted restricted estimation of the parameters and the nonparametric components in the model are constructed based on the theory of the first research and the Lagrange multiplier technique. The hypotheses on the parametric component is considered. A Lagrange multiplier test statistic based on the profile Lagrange multiplier is constructed. The large sample properties of the restricted esti-mation and the test statistics are thoroughly investigated under some regular condition. The finite sample performance of the proposed restricted estimates and the efficiency of the testing method are assessed by some simulation studies.