We consider a blockwise James-Stein estimator for nonparametric function estimation in suitable wavelet or Fourier bases. The estimator can be readily explained and implemented. We show that the estimator is asymptotically sharp-adaptive in minimax risk over any Sobolev ball containing the true function. Further, for a moderately broad range of bounded sets in Besov space our estimator is asymp...

SUMMARY. For a vector of estimable parameters, a modified version of the James-Stein rule (incorporating the idea of preliminary test estimators) is utilized in formulating some estimators based on U-statistics and their jackknifed estimator of dispersion matrix. Asymptotic admissibility properties of the classical U-statistics, their preliminary test version and the proposed estimators are stu...

We construct an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise, using the local and occupation times of Gaussian processes. The method relies on the almost-sure minimization of a Stein Unbiased Risk Estimator (SURE) obtained through integration by parts on Gaussian space, and applied to shrinkage estimators which are constructed by soft and...

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

We give James-Stein type estimators of multivariate normal mean vector by shrinkage to closed convex set K with smooth or piecewise smooth boundary. The rate of shrinkage is determined by the curvature of boundary of K at the projection point onto K . By considering a sequence of polytopes K j converging to K , we show that a particular estimator we propose is the limit of a sequence of estimat...

We consider the problem of efficient estimation for the drift of fractional Brownian motion B := ( B t ) t∈[0,T ] with hurst parameter H less than 1 2 . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

Abstract: The problem of estimating the centre of symmetry of an unknown periodic function observed in Gaussian white noise is considered. Using the penalized blockwise Stein method, a smoothing filter allowing to define the penalized profile likelihood is proposed. The estimator of the centre of symmetry is then the maximizer of this penalized profile likelihood. This estimator is shown to be ...

5.1. Stein’s theorem and the regression model. It was pointed out in Chapter 2, section 2.2, that if no a priori knowledge is specified concerning β, the criterion of minimization of a matrix-valued meansquare error is ill posed. Nevertheless, there are some cases in which the choice of a particular scalar-valued definition of mean-square error makes it possible to obtain estimators with lower ...