Ban Estimation for Chi-Square Test Criteria in Categorical Data

This expository paper describes some recent work that further develops the theory of BAN estimators and the related chi-scuare test statistics.The extensions are in several directions: (a) the class of regular estimators is broadened by permitting extraneous random elements; (b) more general models are permitted under the constraint equations specification; and (c) BAN estimators are defined for general models combining features of two types of specification.In particular, WLS estimators are shown to be BAN.     

Statistical methodology for binary data from a set of partially structured two-way random cross-classifications

A complete two-way cross-classification design is not practical in many settings. For example, in a toxicological study where 30 male rats are mated with 30 female rats and each mating outcome (successful or unsuccessful)is observed, time and resource considerations can make the use of the complete design prohibitively costly. Partially structured variations of this design are, therefore, of interest (e.g., the balanced disjoint rectangle design, the fully diagonal design, and the "S"-design). Methodology for analyzing binary data from such incomplete designs is illustrated with an example. This methodology, which is based on infinite population sampling arguments, allows the estimation of the mean response, among-row correlation coefficient, among-column correlation coefficient, and the within-cell correlation coefficient as well as their standard errors.     

Age-period-cohort analysis: an illustration of the problems in assessing interaction in one observation per cell data

This paper discusses the specific problems of age-period-cohort (A-P-C) analysis within the general framework of interaction assessment for two-way cross-classified data with one observation per cell. The A-P-C multiple classification model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the two-way table) is characterized as one of a special class of models involving interaction terms assumed to have very specific forms. The so-called A-P-C identification problem, which results from the use of a particular interaction structure for detecting cohort effects, is shown to manifest itself in the form of an exact linear dependency among the columns of the design matrix. The precise relationship holding among these columns is derived, as is an explicit formula for the bias in the parameter estimates resulting from an incorrect specification of an assumed restriction on the parameters required to solve the normal equations. Current methods for modeling A-P-C data are critically reviewed, an illustrative numerical example is presented, and one potentially promising analysis strategy is discussed. However, gien the large number of possible sources for error in A-P-C analyses, it is strongly recommended that the results of such analyses be interpreted with a great deal of caution.     

On the asymptotic efficiency of moment and maximum likelihood estimators in the three-parameter inverse gaussian distribution

The asymptotic distribution of estimators generated by the methods of moments and maximum likelihood are considered. Simple formulae are provided which enable comparisons of asymptotic relative efficiency to be effected.     

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 perspective of composite sampling

Composite samples are formed by physically mixing samples. Usually, composite samples are used to reduce the overall cost associated with analytical procedures that must be performed on each sample, but they can also be used to protect the privacy of individuals.

Composite sampling can reduce the cost of identifying individual cases that have a certain trait, such as those with a rare disease or those exceeding pollution-level standards. Not much is lost by applying this method as long as the trait is relatively rare.

Composite sampling can reduce the cost of estimating the mean of some process. When samples are composited, the ability to estimate the variance is lost. In spite of this, the potential savings are so great that composite samples have been used.

Much of this paper deasl with the variance of estimators based on composite sampling when the porportions of hte original samples comprising the composite sample are actually random. Taking repeated samples and measurements on several composite samples complicates the prodcedure, but allows the estimation of between and within variation as well as measurement error.     

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     

Experimental designs and their efficiencies for spatially correlated observations in two dimensions

Optimality of experimental designs for spatially correlated observations is investigated.come two dimensional correlation structures are discussed and an attempt has been made to find optimal or nearly optimal design for each sitution.The solution lend to designs similar to that used for repeated measurements.The relative efficiency of the proposed designs in comparison to randomized latin square designs is tabulated for some cases.     

Local GMM Estimation of Semiparametric Panel Data with Smooth Coefficient Models

In this article, we consider the estimation of semiparametric panel data smooth coefficient models. We propose a class of local generalized method of moments (LGMM) estimators that are simple and easy to implement in practice. We show that the proposed LGMM estimators are consistent and asymptotically normal. Monte Carlo simulations suggest that our proposed estimator performs quite well in finite samples. An empirical application using a large panel of U.K. firms is also presented.     

Parsimonious Estimation of the Covariance Matrix in Multinomial Probit Models

This article presents a Bayesian analysis of a multinomial probit model by building on previous work that specified priors on identified parameters. The main contribution of our article is to propose a prior on the covariance matrix of the latent utilities that permits elements of the inverse of the covariance matrix to be identically zero. This allows a parsimonious representation of the covariance matrix when such parsimony exists. The methodology is applied to both simulated and real data, and its ability to obtain more efficient estimators of the covariance matrix and regression coefficients is assessed using simulated data.