The Tale of Cochran's Rule: My Contingency Table has so Many Expected Values Smaller than 5, What Am I to Do?

In an informal way, some dilemmas in connection with hypothesis testing in contingency tables are discussed. The body of the article concerns the numerical evaluation of Cochran's Rule about the minimum expected value in r × c contingency tables with fixed margins when testing independence with Pearson's X² statistic using the χ² distribution.     

Exact confidence region for the parameters of the gamma distribution based on two independent samples

The gamma distribution has been discussed by many authors. This article proposes an exact confidence region for the parameters of a two-parameter gamma distribution. The result is based on the fact that the percentiles of the F-distribution, with equal degrees of freedom k, are monotonic in k.     

耦合KdV方程组的孤波精确解

本文利用一种简明的方法得出一类耦合KdV方程组的孤波精确解。     

Analysis of the Bovine Spongiform Encephalopathy Maternal Cohort Study: the Discordant Case–Control Pairs

The progeny of the affected and non-affected dams in the bovine spongiform encephalopathy (BSE) cohort study were paired in terms of their farm of origin and approximate date of birth. This paper presents an exact logistic regression analysis that avoids modelling the differences between the pairs and so analyses only the discordant pairs. There is some evidence that the pairs in which the affected animal was born to the affected dam tend to be those in which the onset of BSE in the affected dam preceded or occurred soon after the calving. This suggests some occurrence of maternal transmission.     

Extensions of Fill's algorithm for perfect simulation

Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed.     

Robust modified profile estimating function with application to the generalized estimating equation

We consider methods for reducing the effect of fitting nuisance parameters on a general estimating function, when the estimating function depends on not only a vector of parameters of interest, θ$\theta$, but also on a vector of nuisance parameters, λ$\lambda$. We propose a class of modified profile estimating functions with plug-in bias reduced by two orders. A robust version of the adjustment term does not require any information about the probability mechanism beyond that required by the original estimating function. An important application of this method is bias correction for the generalized estimating equation in analyzing stratified longitudinal data, where the stratum-specific intercepts are considered as fixed nuisance parameters, the dependence of the expected outcome on the covariates is of interest, and the intracluster correlation structure is unknown. Furthermore, when the quasi-scores for θ$\theta$ and λ$\lambda$ are available, we propose an additional multiplicative adjustment term such that the modified profile estimating function is approximately information unbiased. This multiplicative adjustment term can serve as an optimal weight in the analysis of stratified studies. A brief simulation study shows that the proposed method considerably reduces the impact of the nuisance parameters.