In the context of survival analysis it is possible that increasing the value of a covariate "X" has a beneficial effect on a failure time, but this effect is reversed when conditioning on any possible value of another covariate "Y". When studying causal effects and influence of covariates on a...

Based on a model introduced by Kaminsky, Luks, and Nelson (1984), we consider a zero-sum allocation game called the Gladiator Game, where two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's...

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...

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...

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...

This note revisits the problem of selection bias, using a simple binomial example. It focuses on selection that is introduced by observing the data and making decisions prior to formal statistical analysis. Decision rules and interpretation of confidence measure and results must then be taken...

We show in a general setup that if data Y are grouped by a covariate X in a certain way, then under a condition of monotone regression of Y on X, a Simpson’s type paradox is natural rather than surprising. This model was motivated by an observation on recent SAT data which are presented.