On Kernel Density Derivative Estimation Near the Boundary

Abstract

Estimating density derivatives is a powerful technique in statistical data analysis. It has diverse applications in machine learning, signal processing, and statistical analysis. The kernel method is one of the most popular methods in nonparametric density derivative estimation, but this estimator is biased and is not consistent when the data are near the endpoints of the support. This paper investigates the challenge of estimating the first-order derivative of an unknown probability density function defined on the interval [0, 1]. We focus our study near the right boundary. The asymptotic properties are derived. A Monte Carlo study and real data example are provided to illustrate the finite sample performance of the proposed estimator.

Journal of Statistical Research 2025, Vol. 59, No. 2, pp. 183-201