Computation and application of robust data-driven bandwidth selection for gradient function estimation

Abstract

The significance of gradient estimates in nonparametric regression cannot be neglected as it is a critical process for executing marginal effect in empirical application. However, the performance of resulting estimates is closely related to the selection of smoothing parameters. The existing methods of parameter choice are either too complicated or not robust enough. For improving the computational efficiency and robustness, a data-driven bandwidth selection procedure is proposed in this paper to compute the gradient of unknown function based on local linear composite quantile regression. Such bandwidth selection method can solve the difficulty of the infeasible selection program that requires the direct observation of true gradient. Moreover, the leading bias and variance of the estimated gradient are obtained under certain regular conditions. It is shown that the bandwidth selection method processes the oracle property in the sense that the selected bandwidth is asymptotically equivalent to the optimal bandwidth if the true gradient is known. Monte Carlo simulations and a real example are conducted to demonstrate the finite sample properties of the suggested method. Both simulation and application corroborate that our technique delivers more effective and robust derivative estimator than some existing approaches.