A general censoring scheme for circular data

A generalized censoring scheme in the survival analysis context was introduced by the authors in Jammalamadaka and Mangalam [S. Rao Jammalamadaka, V. Mangalam, Nonparametric estimation for middle censored data, J. Nonparametr. Stat. 15 (2003) 253–265]. In this article we discuss how such a censoring scheme applies to circular data and in particular when the original data is assumed to come from a parametric model such as the von Mises. Maximum likelihood estimation of the parameters as well as their large-sample properties are considered under this censoring scheme. We also consider nonparametric estimation of the circular probability distribution under such a general censoring scheme and use Monte Carlo methods to investigate its effects on the estimation of the mean direction and concentration.