We obtain minimax lower bounds on the regret for the classical two--armed bandit problem. We provide a finite--sample minimax version of the well--known log "n" asymptotic lower bound of Lai and Robbins. Also, in contrast to the log "n" asymptotic results on the regret, we show that the minimax...

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the...

To create their rankings, university-ranking agencies usually combine multiple performance measures into a composite index. However, both rankings and index scores are sensitive to the weights assigned to performance measures. This paper uses a stochastic dominance efficiency methodology to...

Using properties of the cdf of a random variable defined as a saddle-type point of a real valued continuous stochastic process, we derive first-order asymptotic properties of tests for stochastic spanning w.r.t. a stochastic dominance relation. First, we define the concept of Markowitz...

I develop a consistent, asymptotically normal estimator of bounds on functions of parameters partially identified by the intersection of continuous linear inequalities. The inference strategy uses results from the semi-infinite programming literature to form a convenient estimator. Aside from...