A more general methodology for fitting global cross-ratio models for discrete longitudinal responses

In this paper, we focus on repeated measurement problems, comprising an interesting research area in statistics. We study longitudinal data which arise when outcomes are observed repeatedly on each experimental subject at several points. We focus on a marginal approach for this type of data with lack of independence among the observations proposed by Dale [Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics. 1986;42(4):909–917] for bivariate, discrete, ordered responses. We propose an alternative estimation based on divergence measures to the full likelihood method proposed in that paper. Finally, a wide simulation study and a data example that illustrates the new methodology is provided.     

The power functions of the likelihood ratio tests for a simply ordered trend in normal means

Likelihood ratio tests for the homogeneity of k normal means with the alternative restricted by an increasing trend are considered as well as the likelihood ratio tests of the null hypothesis that the means satisfy the trend. While the work is primarily a survey of results concerning the power functions of these tests, the extensions of some results to the case of not necessarily equal sample sizes are presented. For the case of known or unknown population variances, exact expressions are given for the power functions for k=3,4, and approximations are discussed for larger k. The topics of consistency, bias and monotonicity of the power functions are included. Also, Bartholomew's conjectures concerning minimal and maximal powers are investigated, with results of a new numerical study given.     

Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

Robust williams trent test

To investigate the biological activities of a new compound or drug, experimenters usually compare a series of increasing doses to a control. Among other objectives, one may try to investigate any possible dose-response trend and to determine the minimum effective dose among all the experimental doses. Williams (1971, 1972) proposed a procedure to test the dose-response trend and also to identify the minimum effective dose based on the normally distributed data. In this paper, we propose a similar test procedure based on the robust estimate'of the average response to perform similar analysis. The proposed method is more resistant to the outliers and more powerful than the Williams procedure when the data distribution deviates from normality. We illustrate the use of this procedure with data arising from a recent study.     

Projectors and linear estimation in general linear models

The paper gives a self-contained account of minimum disper­sion linear unbiased estimation of the expectation vector in a linear model with the dispersion matrix belonging to some, rather arbitrary, set of nonnegative definite matrices. The approach to linear estimation in general linear models recommended here is a direct generalization of some ideas and results presented by Rao (1973, 19 74) for the case of a general Gauss-Markov model

A new insight into the nature of some estimation problems originaly arising in the context of a general Gauss-Markov model as well as the correspondence of results known in the literature to those obtained in the present paper for general linear models are also given. As preliminary results the theory of projectors defined by Rao (1973) is extended.     

The elasticity of labor demand and the minimum wage

We show that, contrary to widespread belief, low-pay workers do not generally prefer that the minimum wage rate be increased until the labor demand is unitary elastic. Rather, there exists a critical value of elasticity of labor demand so that increases in the minimum wage rate make low-pay workers better off for higher elasticities, but worse off for lower elasticities. This critical value decreases with unemployment benefits and increases with workers’ risk aversion. We also show that in some countries the benefits for long-term unemployed are so low that workers would probably prefer that the minimum wage rate be decreased. I thank the anonymous referees for helpful suggestions.     

Relevance of Risk Predictions Derived from a Chronic Species Sensitivity Distribution with Cadmium to Aquatic Populations and Ecosystems

Criteria to protect aquatic life are intended to protect diverse ecosystems, but in practice are usually developed from compilations of single‐species toxicity tests using standard test organisms that were tested in laboratory environments. Species sensitivity distributions (SSDs) developed from these compilations are extrapolated to set aquatic ecosystem criteria. The protectiveness of the approach was critically reviewed with a chronic SSD for cadmium comprising 27 species within 21 genera. Within the data set, one genus had lower cadmium effects concentrations than the SSD fifth percentile‐based criterion, so in theory this genus, the amphipod Hyalella, could be lost or at least allowed some level of harm by this criteria approach. However, population matrix modeling projected only slightly increased extinction risks for a temperate Hyalella population under scenarios similar to the SSD fifth percentile criterion. The criterion value was further compared to cadmium effects concentrations in ecosystem experiments and field studies. Generally, few adverse effects were inferred from ecosystem experiments at concentrations less than the SSD fifth percentile criterion. Exceptions were behavioral impairments in simplified food web studies. No adverse effects were apparent in field studies under conditions that seldom exceeded the criterion. At concentrations greater than the SSD fifth percentile, the magnitudes of adverse effects in the field studies were roughly proportional to the laboratory‐based fraction of species with adverse effects in the SSD. Overall, the modeling and field validation comparisons of the chronic criterion values generally supported the relevance and protectiveness of the SSD fifth percentile approach with cadmium.     

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.