A well-known result by Stein (1956) shows that in particular situations, biased estimators can yield better parameter estimates than their generally preferred unbiased counterparts. This letter follows the same spirit, as we will stabilize the unbiased generalization error estimates by regularization and finally obtain more robust model selection criteria for learning. We trade a small bias aga...

This paper proposes a James-Stein-type (JS) adjustment to analytical bias correction in fixed effects panel models that suffer from the incidental parameters problem. We provide high-level conditions under which infeasible JS leads higher-order MSE improvement over bias-corrected estimator, and former is asymptotically equivalent latter. To obtain feasible adjustment, we propose nonparametric b...

The current standard correlation coefficient used in the analysis of microarray data was introduced by M. B. Eisen, P. T. Spellman, P. O. Brown, and D. Botstein [(1998) Proc. Natl. Acad. Sci. USA 95, 14863-14868]. Its formulation is rather arbitrary. We give a mathematically rigorous correlation coefficient of two data vectors based on James-Stein shrinkage estimators. We use the assumptions de...

Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. In the literature, shrinkage approaches for estimating a high-dimensional covariance matrix are employed to circumvent the limitations of the sample covariance matrix. A new family of nonparametric Stein-type shrinkage covariance estimators is proposed who...

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

The article considers an adaptive sequential nonparametric estimation of a multivariate regression with assigned mean integrated squared error (MISE) and minimax stopping time when the estimator matches performance oracle knowing all nuisance parameters functions. It is known that problem has no solution if belongs to Sobolev class differentiable What underlying smoother, say, analytic? shown i...

In longitudinal imaging studies, geodesic regression in the space of diffeomorphisms [9] can be used to fit a generative model to images over time. The parameters of the model, primarily its initial direction or momentum, are important objects for study that contain biologically meaningful information about the dynamics occurring in the underlying anatomy. Unfortunately, it is common for any gi...

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...

We present a clustering method based on nonparametric density estimation. We use Kernel smoothing and orthogonal series estimators to estimate the density f and then we extract the connected components of the level set using a modified Cuevas et al (2000) algorithm. We extend an idea due to Stein (1981) and Beran and Dümbgen (1998) to construct confidence sets for the level set {f > δc} using t...