This article presents the empirical Bayes method for estimation of the transition probabilities of a generalized finite stationary Markov chain whose ith state is a multi-way contingency table. We use a log-linear model to describe the relationship between factors in each state. The prior...

<Para ID="Par1">Contingency tables are often used to display the multivariate frequency distribution of variables of interest. Under the common multinomial assumption, the first step of contingency table analysis is to estimate cell probabilities. It is well known that the unconstrained maximum likelihood...</para>

In a sample of mRNA species counts, sequences without duplicates or with small numbers of copies are likely to carry information related to mutations or diseases and can be of great interest. However, in some situations, sequence abundance is unknown and sequencing the whole sample to find the...

Recursive formulas are provided for computing probabilities of a multinomial distribution. Firstly, a recursive formula is provided for computing rectangular probabilities which include the cumulative distribution function as a special case. These rectangular probabilities can be used to provide...

We first show that any 1−α bootstrap percentile confidence interval for a proportion based on a binomial random variable has an infimum coverage probability zero for any sample size. This result is then extended to intervals for the difference, the relative risk and the odds ratio of two...

This paper concerns interval estimation for the difference of two dependent proportions. An order on the sample space is constructed using an inductive method; then the smallest one-sided 1−α confidence interval under the order is derived. This interval is admissible under the set inclusion...

An estimator is said to be of orders0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We...

For the first time, explicit expressions are given for the cumulants of the multinomial and the negative multinomial distributions. These expressions are given in terms of Stirling numbers. Computational efficiency of the expressions is illustrated.