Large deviations and moderate deviations for kernel density estimators of directional data (Q1958721)

Let \(f_n\) be the non-parametric kernel density estimator of directional data based on a kernel function \(K\) and a sequence of iid random variables taking values in the \(d\)-dimensional unit sphere \(S^{d-1}\). This paper studies uniform large deviations and uniform moderate deviations for \(f_n\) by the empirical process approach. It is assumed that the kernel is a function of bounded variation and the density of the random variables is continuous.