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

## TL;DR

This paper introduces a novel joint nonparametric method for estimating probability density and its support, effectively addressing boundary bias issues in kernel density estimation, including multivariate cases.

## Contribution

It proposes a boundary detection technique that eliminates boundary bias in kernel density estimation, extending to multivariate scenarios with an improved estimator.

## Key findings

- Successfully detects boundaries in density estimation
- Eliminates boundary bias in univariate and multivariate cases
- Provides a more accurate density and support estimation

## 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.