"Kernel density estimation for polyspherical data and its applications", accepted in the Journal of the American Statistical Association

The paper “Kernel density estimation for polyspherical data and its applications”, coauthored by Eduardo García-Portugués and Andrea Meilán-Vila, has been accepted for publication in the renowned Journal of the American Statistical Association! The preprint can be checked on the arXiv.

The companion R package polykde provides all the methods presented in the paper.

This is the abstract of the paper:

A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean square error, normality, and optimal bandwidths. We address the kernel theory of the estimator beyond the von Mises–Fisher kernel, introducing new kernels that are more efficient and investigating normalizing constants, moments, and sampling methods thereof. Plug-in and cross-validated bandwidth selectors are also obtained. As a spin-off of the kernel density estimator, we propose a nonparametric $k$-sample test based on the Jensen–Shannon divergence that is consistent against alternatives with non-homogeneous densities. Numerical experiments illuminate the asymptotic theory of the kernel density estimator and demonstrate the superior performance of the $k$-sample test with respect to parametric alternatives in certain scenarios. Our smoothing methodology is applied to the analysis of the morphology of a sample of hippocampi of infants embedded on the high-dimensional polysphere $(\mathbb{S}^2)^{168}$ through skeletal representations ($s$-reps).