Density derivative estimation for stationary and strongly mixing data

Abstract

Estimation of density derivatives has found multiple uses in statistical data analysis. An inefficient two-step method to obtain it is estimating the density and then computing the derivatives. This method does not render good results since a good density estimator is not always a suitable density-derivative estimator. The present paper studies the kernel type as a non-parametric estimation of the density function derivative connected with a highly mixing time series. To improve estimation accuracy in asymptotic mean squared error sense, a shrinkage type estimator is defined, under the prior information that the derivative is known. In addition to the investigation of asymptotic distributional properties, a simulation study is carried out to numerically demonstrate the findings. Effect of deviating from the prior information on estimation is also considered and discussed.