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...

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 ...

Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main result is that if G is a locally (soluble-by-finite) group with this property then either G has all subgroups subnormal or G is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same autho...

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...