This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identi…ed with regular bounds. When the bounds are just identi…ed along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an e¢ cient lower bound estimator plus the half of the known interval le...

In this article we study function estimation via wavelet shrinkage for data with long-range dependence. We propose a fractional Gaussian noise model to approximate nonparametric regression with long-range dependence and establish asymp-totics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to zero at rates that diier from those for data...

In this talk I will describe the status of a small test/experiment (T864 (MiniMax)) designed to search for disoriented chiral condensate (DCC) and performed over the last three years at the TeVatron collider. The origins of MiniMax go back earlier to an initiative designed to provide the SSC with a fullacceptance detector (FAD). 1 During the associated workshop activity, it was acutely realized...

This paper considers the minimax filtering problem in which the supremum norm of weighted error sequence is minimized. It is shown that the minimax solution is also the optimal Set-Membership Filtering (SMF) solution. An adaptive algorithm is derived that is based on approximating the minimax cost function at each time instant using an optimal quadratic lower bound. The proposed recursions are ...

Neural networks were evolved through genetic algorithms to focus minimax search in the game of Othello. At each level of the search tree, the focus networks decide which moves are promising enough to be explored further. The networks effectively hide problem states from minimax based on the knowledge they have evolved about the limitations of minimax and the evaluation function. Focus networks ...

It is known that bounds on the minimax values of nodes in a game tree can be used to reduce the computational complexity of minimax search for two-player games. We describe a very simple method to estimate bounds on the minimax values of interior nodes of a game tree, and use the bounds to improve minimax search. The new algorithm, called forward estimation, does not require additional domain k...

The problems of predictive density estimation with Kullback-Leibler loss, optimal universal data compression for MDL model selection, and the choice of priors for Bayes factors in model selection are interrelated. Research in recent years has identified procedures which are minimax for risk in predictive density estimation and for redundancy in universal data compression. Here, after reviewing ...

Neural networks were evolved through genetic algorithms to focus minimax search in the game of Othello. At each level of the search tree, the focus networks decide which moves are promising enough to be explored further. The networks effectively hide problem states from minimax based on the knowledge they have evolved about the limitations of minimax and the evaluation function. Focus networks ...

Consider estimating the mean vector from data Nn( ; I) with lq norm loss, q 1, when is known to lie in an n-dimensional lp ball, p 2 (0;1). For large n, the ratio of minimax linear risk to minimax risk can be arbitrarily large if p < q. Obvious exceptions aside, the limiting ratio equals 1 only if p = q = 2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax ...

New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions, and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of lo...