This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function when 2 is known and unknown. We show that the usual estimator X is minimax and obtain a class of minimax estimators which have uniformly smaller risk than the usual estimator X. Also, we obtain the proper Bayes estimator relative to balanced loss function and nd the minim...

Game-tree pathology is a phenomenon where deeper minimax search results in worse play. It was was discovered 30 years ago (Nau 1982) and shown to exist in a large class of games. Most games of interest are not pathological so there has been little research into searching pathological trees. In this paper we show that even in non-pathological games, there likely are pathological subtrees. Furthe...

the problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including binomial negative binomial discrete weibull and etc., is considered. we give necessary and sufficient conditions for which the bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function. for s...

Markov games are a framework which formalises n-agent reinforcement learning. For instance, Littman proposed the minimax-Q algorithm to model two-agent zero-sum problems. This paper proposes a new simple algorithm in this framework, QL2, and compares it to several standard algorithms (Q-learning, Minimax and minimax-Q). Experiments show that QL2 converges to optimal mixed policies, as minimax-Q...

Recently a numerical calculation method for nding the minimax solution to the minimax problem in quantum signal detection was reported [10]. In this paper, we evaluate the error performance of the minimax receiver for 16QAM coherent state signal by using this calculation method. Through this numerical simulation, it will be pointed out that the use of the minimax strategy has an advantage rathe...

The asymptotic minimax theorem for Bernoulli two-armed bandit problem states that minimax risk has the order N as N → ∞, where N is the control horizon, and provides the estimates of the factor. For Gaussian twoarmed bandit with unit variances of one-step incomes and close expectations, we improve the asymptotic minimax theorem as follows: the minimax risk is approximately equal to 0.637N as N ...

In [14], a new local minimax method that characterizes a saddle point as a solution to a local minimax problem is established. Based on the local characterization, a numerical minimax algorithm is designed for finding multiple saddle points. Numerical computations of many examples in semilinear elliptic PDE have been successfully carried out to solve for multiple solutions. One of the important...

This paper addresses the control design problem for discrete-time, nite-state Markov Decision Processes (MDPs), when both risk-neutral and minimax objectives are of interest. We introduce the mixed risk-neutral/minimax objective, and utilize results from risk-neutral and minimax control to derive an information state process and dynamic programming equations for the value function. We synthesiz...

We study minimax rates of convergence for nonparametric regression and prediction under a random design with dependent errors. It is shown that dependence among errors in general does not hurt a prediction of the next response. For estimating the regression function, however, dependence may damage the minimax rate of convergence. Under the assumption that the errors are independent of the expla...

An A-optimal minimax design criterion is proposed to construct fractional factorial designs, which extends the study of the D-optimal minimax design criterion in Lin and Zhou (Canadian Journal of Statistics 41, 325–340, 2013). The resulting Aoptimal and D-optimal minimax designs minimize, respectively, the maximum trace and determinant of the mean squared error matrix of the least squares estim...