Nonparametric Estimation For Censored Circular Data

TL;DR

This paper introduces a new nonparametric estimator for the probability density function of censored circular data, combining projection and moments methods, with proven convergence rates and demonstrated effectiveness through simulations.

Contribution

It proposes a fully computable quotient estimator specifically designed for censored circular data, with theoretical error bounds and practical validation.

Findings

Derived an upper bound for mean integrated squared error.

Established convergence rates for densities in Sobolev classes.

Validated the estimator's performance through simulations.

Abstract

We study the problem of estimating the probability density function of a circular random variable subject to censoring. To this end, we propose a fully computable quotient estimator that combines a projection estimator on linear sieves with a method-of-moments approach. We derive an upper bound for its mean integrated squared error and establish convergence rates when the underlying density lies in a Sobolev class. The practical performance of the estimator is illustrated through simulated examples.