The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type I and II. The uncertainty classes based on the KL-divergence, αdivergence, symmetrized α-divergence, total variation distance, as well as the band model, moment classes and p-point classes are considered. It is shown with a counterexample that minimax robust tests do no...

This paper provides a direct equivalence proof for minimax solutions of A.I. Subbotin and generalized weak solutions in the sense of idempotent analysis. It is shown that the Hamilton-Jacobi equation Vt+H(t, x,DxV ) = 0 (with the Hamiltonian H(t, x, s) concave in s), considered in the context of minimax generalized solutions, is linear w.r.t. ⊕ = min and ̄ = +. This leads to a representation fo...

This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for th...

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...

In [12], new local minimax theorems which characterize a saddle point as a solution to a two-level local minimax problem are established. Based on the local characterization, a numerical minimax method is designed for finding multiple saddle points. Many numerical examples in semilinear elliptic PDE have been successfully carried out to solve for multiple solutions. One of the important issues ...

We investigate the problem of continuous-time causal estimation under a minimax criterion. Let X = {Xt, 0 ≤ t ≤ T} be governed by the probability law Pθ from a class of possible laws indexed by θ ∈ Λ, and Y T be the noise corrupted observations of X available to the estimator. We characterize the estimator minimizing the worst case regret, where regret is the difference between the causal estim...

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

Game-playing programs usually evaluate moves by searching the game tree using the minimax principle. Practice shows that deeper searches produce better results. However, theoretical analyses indicate that under apparently reasonable conditions, the behavior of minimax is pathological, i.e. deeper searches produce worse results. In this paper, a minimax model that – unlike most work in this area...

In this work we obtain two minimax inequalities in G-convex spaces which extend and improve a large number of generalizations of the Ky Fan minimax inequality and of the von Neumann–Sion minimax principle. © 2005 Elsevier Ltd. All rights reserved.

It is well known that the best equivariant estimator of a variance covari-ance matrix of multivariate normal distribution with respect to the full ane group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a multivari-ate analysis of variance(MANOVA) model and give other classes of minimax estimators.