For general estimable parameters in a nonparametric setup, shrinkage (Stein-rule) and preliminary test estimator versions of U-statistics are considered for the (multi-parameter) minimum risk sequential estimation problem. In the usual fashion, allowing the cost per unit sample to be small, an asymptotic model is framed, and in this setup, the asymptotic distributional risks of these versions o...

Abstract— For audio denoising, diagonal thresholding estimators of spectrogram coefficients produce a “musical noise” that degrades audio perception. We introduce a block thresholding which produces hardly any musical noise and improves the SNR compared to diagonal thresholdings or Ephraim and Malah estimators. Spectrogram coefficients are grouped into blocks to compute attenuation factors. Thi...

Non-Local Means (NLM) and its variants have proven to be effective and robust in many image denoising tasks. In this letter, we study approaches to selecting center pixel weights (CPW) in NLM. Our key contributions are: 1) we give a novel formulation of the CPW problem from a statistical shrinkage perspective; 2) we construct the James-Stein shrinkage estimator in the CPW context; and 3) we pro...

This work consists of developing shrinkage estimation strategies for the multivariate normal mean when covariance matrix is diagonal and known. The domination positive part James–Stein estimator (PPJSE) over (JSE) relative to balanced loss function (BLF) analytically proved. We introduce a new class estimators which ameliorate PPJSE, then we construct series polynomial improve PPJSE; also, any ...

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James–Stein estimators. Both simulated and real data sets are used for illu...

The Fréchet mean is a useful description of location for probability distribution on metric space that not necessarily vector space. This article considers simultaneous estimation multiple means from decision-theoretic perspective, and in particular, the extent to which unbiased estimator can be dominated by generalization James–Stein shrinkage estimator. It shown if satisfies nonpositive curva...

In a system of regression models, finding feasible shrinkage is demanding since the covariance structure unknown and cannot be ignored. On other hand, specifying sub-space restrictions for adequate vital. This study proposes estimation strategies where restriction obtained from LASSO. Therefore, some LASSO-based Stein-type estimators are introduced, their asymptotic performance studied. Extensi...

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from Np+q(μ,Σ), a (p+ q)-dimensional multivariate normal population with mean μ and covariance matrix Σ. On the basis of data consisting of n observations on all p+q characteristics and an additional N − n observations on the last q characteristics, where all observations are mutually independent, denot...

The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function f observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile likelihood with a data-driven penalization is introduced so that the estimator of the center of symmetry is defined as the maximizer of the penalized profile likelihood...