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作者：Bhattacharya, R; Patrangenaru, V
作者单位：Indiana University System; Indiana University Bloomington; University System of Georgia; Georgia State University
摘要：Sufficient conditions are given for the uniqueness of intrinsic and extrinsic means as measures of location of probability measures Q on Riemannian manifolds. It is shown that, when uniquely defined, these are estimated consistently by the corresponding indices of the empirical (Q) over cap (n). Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of (Q) over cap (n) and their asymptotic dispersions are carried out for distributions on the sphe...
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作者：Hoff, PD
作者单位：University of Washington; University of Washington Seattle
摘要：We present a general approach to estimating probability measures constrained to lie in a convex set. We represent constrained measures as mixtures of simple, known extreme measures, and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure. Convex constraints arise in many modeling situations, such as estimation of the mean and estimation under stochastic ordering constraints. We describe mixture representation techniques for these and oth...
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作者：Polzehl, J; Spokoiny, V
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：A new method of pointwise adaptation has been proposed and studied in Spokoiny [(1998) Ann. Statist. 26 1356-1378] in the context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate grey-scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator (f) over cap (x) at a point x is simply the average of observations over a window (U) over cap (x) select...
