Generalized Kernel Regularized Least Squares Estimator with Parametric Error Covariance

A two-step estimator of a nonparametric regression function via KRLS with parametric error covariance is proposed. The KRLS, not considering any information in the error covariance, is improved by incorporating a parametric error covariance, allowing for both heteroskedasticity and autocorrelation, in estimating the regression function. A two step procedure is used, where in the first step, the parametric error covariance is estimated from the residuals obtained by a KRLS regression and in the second step, another KRLS regression based on transformed variables from the error covariance is estimated. Theoretical results including bias, variance, and asymptotics are derived. Simulation results show that the proposed estimator outperforms the KRLS in both heteroskedastic errors and autocorrelated error cases. An empirical example is illustrated with estimating an airline cost function under a random effects model with heteroskedastic and correlated errors. The derivatives are evaluated, and the average partial effects of the inputs are determined in the application.