Suppose you observe a finite sequence of random variables from some known joint distribution F, you can stop the process at any time and your profit is the last observed value. If an optimal stopping rule is used, denote the expected profit by VF. What kind of ordering on multivariate...

An urn contains N balls, labelled 1,...,N. Optimal stopping rules are considered for payoff functions f(k, m) where f(k, m) is the reward when stopping after k draws, and the largest number seen by then is m. f(k, m) is assumed nondecreasing im for each k. We show: (i) For any horizon n...

The problem of finding stopping rules which maximize (EXt) (EYt) is considered, for independent pairs (Xi, Yi) of nonnegative r.v.s. with known joint distribution. The solution is compared to that of maximizing E(Xt Yt). When (Xi, Yi) are uniform, a detailed analysis is given for the...

Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = [Sigma]ni = 1 Cov(X1, Xi)P(Xi = X(1)), where X(1) is the minimum of (X1, ..., Xn). We show that a similar result holds for any order statistic. Thus X(1)...

Consider a production process where the categories of successive units form a Markov chain with known transition matrix. Whenever a unit is produced, we may, at a fixed cost, inspect it. If its value is less than maximal, we may replace it with a perfect (maximal value) unit. We obtain optimal...

We consider the best-choice secretary problem, with a known number, n, of applicants, and a random, independent "freeze" variable M, with known distribution. No hiring is possible after time M. The goal is to choose the best among the n applicants, where the decisions must be made depending only...

It is shown that if Xk satisfy P(Xk ak|X1 a1,..., Xk-1 ak-1) is nondecreasing in a1,..., ak-1, a negative dependence condition slightly weaker than CDS, and 0 [less-than-or-equals, slant] Xk [less-than-or-equals, slant] 1, then E[max Xk] [less-than-or-equals, slant] 2V - V2, where V = sup...