A note on density estimation for circular data

Abstract

We discuss kernel density estimation for data lying on the d-dimensional torus (d ≥ 1). We consider a specific class of product kernels, and formulate exact and asymptotic L 2 properties for the estimators equipped with these kernels. We also obtain the optimal smoothing for the case when the kernel is defined by the product of von Mises densities. A brief simulation study illustrates the main findings.