Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

2016/01/19 by Yogendra P. Chaubey, Chaubey, Yogendra P.
Computer Science · Mathematics · #62G07 #62H11 #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Statistics Theory (math.ST) #math.ST #msc:62G07 #msc:62H11 #stat.TH

paper · pdf · doi:10.48550/arxiv.1601.05053

9 pages

arxiv created 2016/01/19 · openalex publication_date 2016/01/19 · arxiv updated 2016/01/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this note we provide a simple approximation theory motivation for the circular kernel density estimation and further explore the usefulness of the wrapped Cauchy kernel in this context. It is seen that the wrapped Cauchy kernel appears as a natural candidate in connection to orthogonal series density estimation on a unit circle. This adds further weight to the considerable role of the wrapped Cauchy in circular statistics.

Related

• A reliable data-based smoothing parameter selection method for circular kernel estimation
• Spline Smoothing for Estimation of Circular Probability Distributions via Spectral Isomorphism and its Spatial Adaptation
• Circular and Spherical Projected Cauchy Distributions: A Novel Framework for Circular and Directional Data Modeling
• Adaptive Density Estimation on the Circle by Nearly-Tight Frames
• Nonparametric Estimation For Censored Circular Data