We consider the classical problem of selecting the best of two treatments in clinical trials with binary response. The target is to find the design that maximizes the power of the relevant test. Many papers use a normal approximation to the power function and claim that Neyman allocation that...

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...

We study estimation of finite population quantiles, with emphasis on estimators that are invariant under monotone transformations of the data, and suitable invariant loss functions. We discuss non-randomized and randomized estimators, best invariant and minimax estimators and sampling strategies...

Phase I clinical trials are conducted in order to find the maximum tolerated dose (MTD) of a given drug from a finite set of doses. For ethical reasons, these studies are usually sequential, treating patients or group of patients with the best available dose according to the current knowledge....

A population that can be joined at a known sequence of discrete times is sampled cross-sectionally, and the sojourn times of individuals in the sample are observed. It is well known that cross-sectioning leads to length-bias, but less well known that it may result also in dependence among the...

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...

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.

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>