Large sample bias of maximum likeihood estimates from a series of sparse ixj tables

For a large series of IxJ tables, each containing two observations, the bias of the maximum likelihood estimates of log linear partial association parameters is shown to be equal to the parameters, regardless of the size of I and J. The partial association considered is that between row and column variables; the three way interactions are assumed to be O. This is a generalization of Andersen's results (1973a, 1973b) for a series of 2x2 tables.     

Conditions for fourth order rotatability in K dimensions

In this paper, conditions for a set of points to form a rotatable design of order four have been worked out. These condi- tions form the basis for obtaining a set of rotatable designs of order four.     

A new rank test for the K-Sample problem

The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution     

An emplrical bayes approach in estimating the parameters of the or more geometric distributions

The estimation of the parameters of two or more geometric distribuionsis considered by usinq an empirical Bayesian approach. Robbins (1983) gave empirical Bayes estimates if the number of distributions N is large, buthere we consider the cascwhore N is small. The parameters of the prior distribution areest imated by looking at maximum like lihood and momentest imation methods.     

Order statistics from the linear-exponential distribution,part I: increasing hazard rate case

For the linear-exponential distribution with increasing hazard rate, exact and explicit expressions for means, product moments and percentage points of order statistics are obtained. Some recurrence relations for both single and product moments of order statistics are also derived. These recurrence relations would enable one to obtain all the higher order moments of order statistics for all sample sizes from those of the lower order     

Moments for a ratio of correlated gamma variates

This paper considers the finite integral moments for the ratio, R = X/Y, where X and Y re correlated gamma distributed variables. An analytical and numerical comparison is given for two classes of underlying bivariate gamma distributions. It is shown that the two bivariate gamma structures provide indentical experessions for the mth unadjussted moment, E(R^m), if and only if either of the following conditions hold : 1) X and Y are uncorrelated of 2) m=1. A numerical evaluation is performed to determine the extent that the two methods differ whenever the variables are correlated     

A prior-valued estimator applied to multinomial classification

A multinomial classification rule is proposed based on a prior-valued smoothing for the state probabilities. Asymptotically, the proposed rule has an error rate that converges uniformly and strongly to that of the Bayes rule. For a fixed sample size the prior-valued smoothing is effective in obtaining reason¬able classifications to the situations such as missing data. Empirically, the proposed rule is compared favorably with other commonly used multinomial classification rules via Monte Carlo sampling experiments     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.     

The poisson-inverse gaussian disiribuiion as a model for species abundance

An inverse Gaussian mixture of Poisson distributions(the P-IG distribution) is considered as a model for species abundance data,, Minimum chi-square and maximum likelihood methods of estimation for the zero-truncated P-IG distribution are developed, Ihe performance of the P-IG distribution is illustrated and discussed for several well-known sets of insect abundance data.     

A four-moment approach and other practical solutions to the behrens-f1sher problem

Fixed sample size approximately similar tests for the Behrens-Fisher problem are studied and compared with various other tests suggested in current sttistical methodelogy texts. Several fourmoment approxiamtely similar tests are developed and offered as alternatives. These tests are shown to be good practical solutions which are easily implemented in practice.