This paper examines the estimation of an indirect signal embedded in white noise on vector bundles. It is found that the sharp asymptotic minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus when the linear operator has polynomial decay,...

This paper proposes nonparametric deconvolution density estimation overS2. Here we would think of theS2elements of interest being corrupted by randomSO(3) elements (rotations). The resulting density on the observations would be a convolution of theSO(3) density with the trueS2density....

This paper examines the estimation of an indirect signal embedded in white noise for the spherical case. It is found that the sharp minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus, when the linear operator has polynomial decay,...

This paper addresses the issue of optimal deconvolution density estimation on the 2-sphere. Indeed, by using the transitive group action of the rotation matrices on the 2-dimensional unit sphere, rotational errors can be introduced analogous to the Euclidean case. The resulting density turns out...

The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim...

Spherical regression in a decision theoretic framework is examined, where the data is observed on S2 with the parameter space being SO(3). Bayes estimators are characterized under squared error loss on SO(3) as well as conditions under which the least squares estimator is a Bayes estimator with...

It is common to reduce the dimensionality of data before applying classical multivariate analysis techniques in statistics. Persistent homology, a recent development in computational topology, has been shown to be useful for analyzing high-dimensional (nonlinear) data. In this article, we...

Microarray experiments have raised challenging questions such as how to make an accurate identification of a set of marker genes responsible for various cancers. In statistics, this specific task can be posed as the feature selection problem. Since a support vector machine can deal with a vast...