Density estimation for circular data observed with errors

Until now the problem of estimating circular densities when data are observed with errors has beenmainly treated by Fourier series methods. We propose kernel-based estimators exhibiting simple construction and easyimplementation. Specifically, we consider three different approaches: the first one is based on the equivalence betweenkernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored,despite its potential for application also in the Euclidean setting. The second approach relies on estimators whoseweight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires adhoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimatorswhich use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all theproposed estimators we derive asymptotic properties, provide some simulation results, and also discuss some possiblegeneralizations and extensions. Real data case studies are also included.