Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition

This paper studies the estimation and testing problems for a class of heteroscedastic semi-varying coefficient errors-in-variables models under additional restricted condition. Initial restricted estimates for the regression coefficients and varying coefficients are first constructed based on the profile least squares procedure without considering the heteroscedasticity, then a bias-corrected kernel type restricted estimate for the variance function is proposed, which in turn is used to construct re-weighted bias-corrected restricted estimates of the regression coefficients and the varying coefficients. The large sample properties including the consistency and asymptotic normality are thoroughly investigated. To test hypotheses on the parametric component, we propose a test statistic based on the profile Lagrange multiplier, and show that its asymptotic null distribution is standard chi-squared distribution. Some simulation studies are conducted to evaluate the finite sample performance of the proposed methods.