A problem of optimally allocating partially effective ammunition x to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time t, known as the Bomber Problem, was first posed by Klinger and Brown (1968). They conjectured a set of apparently...

We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount x of ammunition is intercepted by enemy airplanes arriving according to a homogenous Poisson process over a fixed time...

We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null hypothesis where there is no distinguished pairing of the...

The inequality conjectured by van den Berg and Kesten in [9], and proved by Reimer in [6], states that for A and B events on S, a product of finitely many finite sets, and P any product measure on S,P(AÊB) <FONT FACE="Symbol">£</FONT> P(A)P(B), where AÊB are the elementary events which lie in both A and B for `disjoint...</font>

We compare estimators of the (essential) supremum and the integral of a function f defined on a measurable space when f may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that...

Statistical models in econometrics, biology, and most other areas, are not expected to be correct, and often are not very accurate. The choice of a model for the analysis of data depends on the purpose of the analysis, the relation between the data and the model, and also on the sample or data...

A stationary renewal process based on iid random variables $X_i$ is observed at a given time. The excess time, that is, the residual time until the next renewal event, is of course smaller than the total current $X$ which consists of the residual time plus the current age. Nevertheless in...

In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X...