Estimating a Distribution Function at the Boundary

Austrian Journal of Statistics

article

Shunpu Zhang¹  Zhong Li²  Zhiying Zhang² 

[1] University of Central Florida;Zhejiang Sci-Tech University

关键词: boundary distribution kernel;    distribution function estimation;    integrated meansquared error;    kernel estimator;    mean squared error.;   

DOI  :  10.17713/ajs.v49i1.801

学科分类：医学（综合）

来源: Austrian Statistical Society

【 摘 要 】

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

【 授权许可】

CC BY