A bivariate density estimation method based on level crossings

作者：Huang Mei Ling^*; Yuen Wai Kong

来源：Statistics, 2010, 44(1): 31-55.

DOI：10.1080/02331880902757831

• efficiency
• bivariate sample level crossing function
• nonparametric functional estimation
• bivariate order statistics

This article introduces a method of nonparametric bivariate density estimation based on a bivariate sample level crossing function, which leads to the construction of a bivariate level crossing empirical distribution BLCEDF). An efficiency function for this BLCEDF relative to the classical empirical distribution EDF), is derived. The BLCEDF gives more efficient estimates than the EDF in the tails of any underlying continuous distribution, for both small and large sample sizes. On the basis of BLCEDF we define a bivariate level crossing kernel density estimator (BLCKDE) and study its properties. We apply the BLCEDF and BLCKDE for various distributions and provide results of simulations that confirm the theoretical properties. A real-world example is given.

• 出版日期2010