A new method of joint nonparametric estimation of probability density and its support

Abstract

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density is not the whole real line. To avoid the unknown boundary effects, our estimator detects the boundary, and eliminates the boundary-bias of the estimator simultaneously. Moreover, we refer an extension to a simple multivariate case, and propose an improved estimator free from the unknown boundary bias