This paper addresses an estimation problem of an additive functional of φ, which is defined as θ(P ;φ) = ∑ k i=1 φ(pi), given n i.i.d. random samples drawn from a discrete distribution P = (p1, ..., pk) with alphabet size k. We have revealed in the previous paper [1] that the minimax optimal rate of this problem is characterized by the divergence speed of the fourth derivative of φ in a range o...

A fundamental quantity in statistical decision theory is the notion of the minimax risk as5 sociated with an estimation problem. It is based on a saddlepoint problem, in which nature plays the 6 role of adversary in choosing the underlying problem instance, and the statistician seeks an estimator 7 with good properties uniformly over a class of problem instances. We argue that in many modern 8 ...

We investigate minimax Latin hypercube designs in two dimensions for several distance measures. For the `-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n. For the `1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n....

Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs. It is well known, however, to be extremely sensitive to outliers in the data resulting, e.g., of sensor failures. In this paper, a new method is proposed to robustify minimax estimation b...

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...