A. Meilán-Vila, E. García Portugués
Polyspherical data refer to observations on S^d_1 × … × S^d_r, d_1,…,d_r ≥ 1, where S^d denotes the hypersphere of dimension d ≥ 1. The polysphere comprises the circle (r=d_1=1), sphere (r=1, d_1=2), and torus (d_1=… =d_r=1), as particular cases. The goal of this work is to propose and study a kernel density estimator for this type of data. Using a tailored tangent-normal decomposition, the main asymptotic properties of the estimator, such as bias, variance, pointwise normality, and optimal bandwidth, are obtained. Some guidelines, based on cross-validation and plug-in methods, to select the asymptotically optimal bandwidth parameter are also provided in practice. Moreover, the kernel efficiency with respect to a certain "Epanechnikov" kernel is studied. A simulation study and an application of the methodology to the hippocampus via s-reps on the polysphere (S^d_1)^{168} complete this work.
Keywords: Directional Data, Nonparametric Statistics, Density Estimator, s-reps
Scheduled
GT18 Non-parametric statistics II. Nonparametric inference for density and distribution
June 9, 2022 12:00 PM
A15
