We propose a sharp change point estimator based on the differences between right and left boundary wavelet smoothers. It is constructed by applying a two-step procedure to the observed data and has the minimax convergence rate. Next, we estimate the regression function with boundary wavelets in...

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 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,...

We consider bivariate logspline density estimation for tomography data. In the usual logspline density estimation for bivariate data, the logarithm of the unknown density function is estimated by tensor product splines, the unknown parameters of which are given by maximum likelihood. In this...

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...

A kernel regression estimator is proposed wherein the regression function is smooth, except possibly for a finite number of points of discontinuity. The proposed estimator uses preliminary estimators for the location and size of discontinuities or change-points in an otherwise smooth regression...

We show that a bootstrap model selection criterion constructed by directly plugging-in a consistent estimator in place of the unknown parameter has a downward bias of amount roughly equivalent to the number of parameters in the approximating model. An example is provided to illustrate the points...

This paper proposes a new B-spline method for nonparametric regression function estimation which can be applied to the case even when the covariate is contaminated with noise. A property of B-splines, reproducing line property, is crucial in the construction of B-spline estimators for regression...