The authors propose and explore new regression designs. Within a particular parametric class, these designs are minimax robust against bias caused by model misspecification while attaining reasonable levels of efficiency as well. The introduction of this restricted class of designs is motivated by a desire to avoid the mathematical and numerical intractability found in the unrestricted minimax ...

In the context of testing the speci cation of a nonlinear parametric regression function, we study the power of speci cation tests using the minimax approach. We determine the maximum rate at which a set of smooth local alternatives can approach the parametric model while ensuring consistency of a test uniformly against any alternative in this set. We show that a smooth nonparametric testing pr...

Stackelberg security games (SSGs) have been deployed in a number of real-world domains. One key challenge in these applications is the assessment of attacker payoffs, which may not be perfectly known. Previous work has studied SSGs with uncertain payoffs modeled by interval uncertainty and provided maximin-based robust solutions. In contrast, in this work we propose the use of the less conserva...

Robust synthesis is one of the remaining challenges in model predictive control (MPC). One way to robustify an MPC controller is to formulate a minimax problem, i.e., optimize a worst-case performance measure. For systems modeled with an uncertain gain, there are many results available. Typically, the minimax formulations have given intractable problems, or unorthodox performance measures have ...

We introduce a notion of ‘relative redundancy’ for universal data compression and propose a universal code which asymptotically achieves the minimax value of the relative redundancy. The relative redundancy is a hybrid of redundancy and coding regret (pointwise redundancy), where a class of information sources and a class of codes are assumed. The minimax code for relative redundancy is an exte...

This paper investigates the ability of the Particle Swarm Optimization (PSO) method to cope with minimax problems through experiments on well{known test functions. Experimental results indicate that PSO tackles minimax problems e ectively. Moreover, PSO alleviates di culties that might be encountered by gradient{based methods, due to the nature of the minimax objective function, and potentially...

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, O(n log n)-time algorithm for building them. Drmota and Szpankowski (2002) gave another O(n log n)-time algorithm, which takes linear time when th...

the problem of density estimation on R from an independent sample X1, ...XN with common density f is concerned. The behavior of the minimax Lp-risk, 1 ≤ p ≤ ∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is provided. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator...

This paper introduces a formulation of the mixed risk-neutral/minimax control problem for Markov Decision Processes (MDPs). Drawing on results from risk-neutral control and minimax control, we derive an information state process and dynamic programming equations for the value function. Furthermore, we develop a methodology to synthesize an optimal control law on the nite horizon, and a near-opt...

The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behavior ...