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...

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,...

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...

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 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...

In this paper, the authors considered various procedures for testing for the independence of two multivariate regression equations with different design matrices. Asymptotic null distributions as well as nonnull distributions under local alternatives of the test statistics associated with the...

This paper considers the problems of estimating a mean vector [mu] under constraint [mu]'[Sigma]-1[mu] = 1 or [Sigma]-1/2[mu] = c and derives the best equivariant estimators under the loss (a - [mu])' [Sigma]-1(a - [mu]), which dominate the MLE's uniformly. The results are regarded as...

Let Rn-p, (n), Gl(p) and +(p) denote respectively the set of n-p matrices, the set of n-n orthogonal matrices, the set of p-p nonsingular matrices and the set of p - p positive definite matrices. In this paper, it is first shown that a bijective and bimeasurable transformation (BBT) g on...

This paper considers the problem of estimating the coefficient matrix B: m - p in a normal multivariate regression model under the risk matrix : m - m and obtains classes of minimax estimators for Baranchik type, Strawderman type, Efron-Morris type, and Stein type estimators.