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Recently, variational Bayesian (VB) techniques have been applied to probabilistic matrix factorization and shown to perform very well in experiments. In this paper, we theoretically elucidate properties of the VB matrix factorization (VBMF) method. Through finite-sample analysis of the VBMF estimator, we show that two types of shrinkage factors exist in the VBMF estimator: the positive-part Jam...

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic...

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...

This paper addresses the problems of estimating the normal covariance and precision matrices. A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators. The class shows inadmissibility of the best invariant and minimax estimator of the covariance matrix relative to quadratic loss. Also, in estimation of the precision matrix, a dominance result...

The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. Although a standard loss function is the Stein loss, it is not available in the case of a high dimension. In this paper, a new type of a quadratic loss function, called the intrinsic loss, is suggested, and unified dominance results are derived under the loss, i...