`p-norm based James-Stein estimation with minimaxity and sparsity

Prediction of blood cancer using leukemia gene expression data and sparsity-based gene selection methods

Background: DNA microarray is a useful technology that simultaneously assesses the expression of thousands of genes. It can be utilized for the detection of cancer types and cancer biomarkers. This study aimed to predict blood cancer using leukemia gene expression data and a robust ℓ2,p-norm sparsity-based gene selection method. Materials and Methods: In this descriptive study, the microarray ...

Integral Inequality for Minimaxity in the Stein Problem

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...

Stochastic analysis on Gaussian space applied to drift estimation

In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Loève expansions. We construct efficient estimators for the drift of such processes, and prove their minimaxity using Bayes estimators. We also construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and s...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Adapting to Unknown Sparsity by controlling the False Discovery Rate

We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the lp norm for p small. We obtain a procedure which is ...