Bernstein Polynomial Model for Multivariate Density

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zhong Guan*+
• Companies: Indiana University, South Bend
• Keywords: Multivariate density estimation ; Bernstein polynomials ; Beta mixture ; Maximum likelihood ; EM Algorithm ; Parameterization

Abstract

In this paper, we generalize the Bernstein polynomial likelihood to the multivariate distribution on $[0,1]^d$ using the iterated multivariate Bernstein polynomials. As a mixture model of multivariate beta distributions, the maximum likelihood estimate can be obtained using EM algorithm. Methods of choosing optimal degree of the Bernstein polynomials based on Kolmogorov-Smirnov statistic and the integrated square error of the density estimate are also presented. The method is applied to estimate the joint density function and the joint cumulative distribution function. Simulation study shows that one can benefit from both the smoothness and the accuracy by using the proposed method.