Abstract

Density estimation of circular data with Bernstein polynomials

Abstract

This paper introduces a new, non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities. The model generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular data. In particular, it is shown that the trigonometric moments of the proposed circular Bernstein polynomial distribution can all be derived in closed form. Secondly, we introduce an approach to circular Bernstein polynomial density estimation given a sample of data and examine the properties of this estimator. Finally our method is illustrated with a simulation study and a real data example.

Keywords

• circular data,non-parametric modeling,Bernstein polynomials

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