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...

WILLIAM BECKNER Abstract. Sharp Lp extensions of Pitt’s inequality expressed as a weighted Sobolev inequality are obtained using convolution estimates and Stein-Weiss potentials. Optimal constants are obtained for the full Stein-Weiss potential as a map from Lp to itself which in turn yield semi-classical Rellich inequalities on Rn. Additional results are obtained for Stein-Weiss potentials wit...

Sharp tail asymptotics are established for generalized Heston and Stein-Stein stochastic volatility models, with a perturbed drift for the volatility process. This builds on the work of Gulisashvili&Stein[Gul10],[GS10][GS10I] and Friz et al.[FGGS10], [DFJV11].

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 propose a new ridge-type estimator called the new mixed ridge estimator (NMRE) by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) against th...

In 1958, Irving Freiler Stein Sr. published ?The Stein-Leventhal Syndrome: A Curable Form of Sterility? documenting his findings on the diagnosis and surgical treatment of Stein-Leventhal syndrome. Stein-Leventhal syndrome, later called polycystic ovarian syndrome (PCOS), affects the reproductive health of women. Common symptoms include excess body hair, a lack of menstrual cycle or amenorrhea,...

1 Stein’s lemma • In a landmark paper, Stein (1981) derived a beautiful and simple lemma about the standard normal distribution. Indeed, Stein knew of this result much earlier and wrote about it in previous papers, but in Stein (1981), the author developed a multivariate extension of this lemma that led to a remarkable result on unbiased risk estimation. (And, an interesting note: the paper Ste...

Here we prove that a compact Stein manifoldW 2n+2 of dimension 2n+2 > 4 admits a Lefschetz fibration over the disk D with Stein fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of “generalized Dehn twists” along imbedded n-spheres on the generic fiber. Also, the open book on the boundary ∂W , which is determined by the fibration, is compatible with...

This result has been extended to open sets in Stein manifolds. But nothing is known about this if (Dj)j≥1 is a family of a Stein complex space X, even when X has isolated singularities. The main new result of this article concerns a generalization of this theorem for families of q-complete open sets in Stein spaces. By using a description of q-convex functions in terms of linear sets, introduce...