The conditional MLE in the two-parameter geometric distribution and its competitors

The conditional maximum likelihood estimator of the shape parameter in the two-parameter geometric distribution is introduced and explored. The estimator is compared with the unconditional maximum likelihood estimator and the uniformly minimum variance unbiased estimator.     

Systematic and nonrandom sampling in the presence of polynomial trends

In the case of finite populations with low-order polynomial trends present, the use of the least squares regression estimator of the mean is discussed. A sampling scheme, which optimizes the efficiency of the regression estimator over a particular class of schemes, is presented.     

Limiting admissible estimators for variance components

Simultaneous estimation of the vector of the variance components for mixed and random models under the quadratic loss function is considered. For a large class of such models there are identified classes of admissible biased invariant quadratic estimators that are better than some admissible unbiased estimators. Numerous numerical results presented in the paper show that for many of the commonly used balanced models the improvements in the quadratic risk may be considerable over a large set of the parameter space.     

The estimation of exchangeable binomial parameters

A general class of Bayesian estimators for several Binomial parameters is proposed. The estimati on procedures are based on a logistic transformation of the parameters and a class of symmetric prior distributions.     

Simultaneous estimation of gamma means using a hierarchical generalized linear model

The problem of simultaneously estimating p Gamma means is investigated when the means are believed a priori to satisfy an r-dimensional generalized linear model. Using a Bayesian hierarchical model to reflect the uncertainty in the linear model, approximate methods are proposed to compute the posterior densities. The resulting estimator shrinks the usual estimator toward a prior estimator where the size of the shrinkage depends upon the agreement of the observed data with the proposed generalized linear model.     

Further results on the two-stage hierarchial information (2shi) estimators in the linear regression models

The paper considers a class of 2SHI estimators for the linear regression models and provides some results regarding the dominance in quadratic loss of this class over the OLS and usual Stein-rule estimators.     

The centered normal conditionals distribution

In this paper, we discuss some aspects of the distribution theory associated with the centered bivariate normal conditionals distribution including discussion of its marginal distributions. We calculate the maximum likelihood and pseudolikelihood estimators. We propose a simplified moment based method of estimation. Finally, we discuss generalizations to higher dimensions.     

Combining estimators from variety trials that are connected by control varieties only

At one site and year often numerous variety trials are performed. Sometimes these trials only have a small number of control varieties in common. It is possible to obtain best linear unbiased estimators (BLUEs) of estimable linear combinations of the variety parameters without analysing the joint observations of all trials as a whole. The unbiased local estimator of the contrast between the parameter of a new variety and the average of the parameters of the control varieties, calculated at a single trial, can be improved to the BLUE with information from the other trials. This improvement represents a contrast of contrasts between control variety parameters at the various trials. In some situations the local estimator is already the BLUE, e.g. if only one control variety is used or in case of variance-balanced designs.