In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or disco...

We present a multi-task learning approach to jointly estimate the means of multiple independent distributions from samples. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the individual task’s sample averages. We derive the optimal amount of regularization for the two task case for the minimum risk estimator and a minimax estimator, and show that the optima...

Smooth James-Stein thresholding-based estimators enjoy smoothness like ridge regression and perform variable selection like lasso. They have added flexibility thanks to more than one regularization parameters (like adaptive lasso), and the ability to select these parameters well thanks to a unbiased and smooth estimation of the risk. The motivation is a gravitational wave burst detection proble...

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in interval (0, 1), such as rates, proportions, percentages fractions. Generally, parameters of BRM are estimated by method maximum likelihood estimation (MLE). However, MLE does not offer accurate reliable estimates explanatory variables correlated. To solve this problem, ridge Liu est...

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...

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 James-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 ...

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 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...