Estimation of the Minimum of a Function Using Order Statistics

Suppose A is a bounded set in ℛ d and f a real function defined on A. Suppose m = min{f(x; | x ∈ A} exists. Using a random sample X 1, X 2. …, X n from a uniform distribution over A we construct a confidence interval for m using asymptotic theory. Our results contain some statistical results valid in general extreme value theory (estimation of the main parameter of extreme value distributions).