Details of Research Outputs

Error variance estimation plays a key role in the analysis of homogeneous non-parametric regression models. For a random design model, most methods in the literature for error variance estimation assume the independence between the predictor variable X and the error ε. In this work, we derive the optimal semi-parametric efficiency bound for the error variance (Formula presented.) without such an independence assumption. A residual-based efficient estimator for (Formula presented.) is proposed and its asymptotic normality is established. An extensive simulation study is conducted, which shows that our proposed estimator works very favourably against competitors. A simple real-data example is also presented.