P erhaps the most surprising result in Statistics arises in a remarkably simple estimation problem. Let X1, ..., Xp be independent random variables, with Xi ∼ N(θi , 1) for i = 1, ..., p. Writing X = (X1, ..., Xp), suppose we want to find a good estimator θ̂ = θ̂(X) of θ = (θ1, ..., θp). To define more precisely what is meant by a good estimator, we use the language of statistical decision theory...

Policy gradient methods have been successfully applied to many complex reinforcement learning problems. However, policy gradient methods suffer from high variance, slow convergence, and inefficient exploration. In this work, we introduce a maximum entropy policy optimization framework which explicitly encourages parameter exploration, and show that this framework can be reduced to a Bayesian in...

In 1961, James and Stein discovered a remarkable estimator that dominates the maximum-likelihood estimate of the mean of a p-variate normal distribution, provided the dimension p is greater than two. This paper extends the James–Stein estimator and highlights benefits of applying these extensions to adaptive signal processing problems. The main contribution of this paper is the derivation of th...

Department of Cardiology and Pulmonary Medicine University of Göttingen Robert Koch Strasse 40 D-37099 Göttingen, Germany e-mail: katrin.schaefer@ med.uni-goettingen.de

—Competition with gizzard shad Dorosoma cepedianum has been shown to influence survival of larval bluegills Lepomis macrochirus as well as growth and size structure of largemouth bass Micropterus salmoides, which prey on these planktivorous species. However, little is known about how the presence of gizzard shad influences bluegills beyond the larval stage. We examined bluegill–gizzard shad int...

We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals. AMS 2000 subject classifications: Primary 60K35; secondary 94A17.

The Stein-Lovász Theorem can be used to get existence results for some combinatorial problems using constructive methods rather than probabilistic methods. In this paper, we discuss applications of the Stein-Lovász Theorem to some combinatorial set systems and arrays, including perfect hash families, separating hash families, splitting systems, covering designs, lotto designs and ∆-free systems...

An approach is presented to get interconnections between the Fisher information matrix of an ARMAX process and a corresponding solution of a Stein equation. The case of algebraic multiplicity greater than one and the case of distinct eigenvalues are addressed. Appropriate links are constructed for these two cases by applying a factorization both for the Fisher information matrix and for a corre...