New classes of density estimates of low bias

A desirable property of a kernel used for a density estimate is that it has high order as this gives low bias. Given a kernel K, a basis {pj(z), j >= 0}, and q >= 1, we show how to choose a = (a0, ... , aq-1)' such that Kq(z) = K(z) sigma q-1 j=0 ajpj(z) is a kernel of order at least q. a is given in terms of the mixed moments, E [Zj pk(Z)]. Some of the kernels involve the complex unit. A simulation study is performed to compare density estimates based on some of the proposed kernels to competitive ones including those in Withers and Nadarajah [1]. The proposed estimates are shown to have smaller biases and smaller mean squared errors.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

A desirable property of a kernel used for density estimation is high order to reduce bias. This study shows how to choose coefficients a to construct a kernel function of at least order q. The coefficients a are obtained through calculation of mixed moments. A simulation study compares density estimates based on the proposed kernels to competitive methods, and the results show that the proposed methods have smaller biases and mean squared errors.