On sequential minimax

Sequential Minimax Search for a Maximum

The problem formulated below was motivated by that of determining an interval containing the point at which a unimodal function on the unit interval possesses a maximum, without postulating regularity conditions involving continuity, derivatives, etc. Our solution is to give, for every e > 0 and every specified number N of values of the argument at which the function may be observed, a procedur...

Nearly Minimax One-Sided Mixture-Based Sequential Tests

We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases—either a discrete alternative or a continuous alternative that can be embedded into an exponential family. For each case, we find a mixture-based stopping rule that is nearly minimax in the sense of minimizing t...

Applying the Minimax Principle to Sequential Mastery Testing

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master, a nonmaster, or to continue sampling and administering another random item. The framework of minimax sequential decision theory (minimum information approach) is used; that is, optimal rules are obtained by minimizing the maximum exp...

Sequential Minimax Search for a Zero of a Convex Function

On minimax density estimation on R

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...