A Comparison of Partially Adaptive and Reweighted Least Squares Estimation

The small sample performance of least median of squares, reweighted least squares, least squares, least absolute deviations, and three partially adaptive estimators are compared using Monte Carlo simulations. Two data problems are addressed in the paper: (1) data generated from non-normal error distributions and (2) contaminated data. Breakdown plots are used to investigate the sensitivity of partially adaptive estimators to data contamination relative to RLS. One partially adaptive estimator performs especially well when the errors are skewed, while another partially adaptive estimator and RLS perform particularly well when the errors are extremely leptokur-totic. In comparison with RLS, partially adaptive estimators are only moderately effective in resisting data contamination; however, they outperform least squares and least absolute deviation estimators.     

Sources of family violence

This paper suggests a direction for the exploration of the causes of family violence. Explanatory models of family violence were considered in this regard, with the recommendation that a multi-determined model should be considered to ensure the most accurate explanation. We suggest that family violence will be best understood and prevented or alleviated, if a model is used that considers the interaction of structural violence and the personality features of all the family members.     

On the existence and uniqueness of maximizers of two likelihood functions

While applying theclassical maximum likelihood method for a certain statistical inference problem, Smith and Weissman [5] have noted that there are conditions under which the likelihood function may be unbounded above or may not possess local maximizers. Ariyawansà and Templeton [1] have derived inference procedures for this problem using the theory of structural inference [2,3,4]. Based on numerical experience, and without proof, they state that the resulting likelihood functions possess unique, global maximizers, even in instances where the classical maximum likelihood method fails in the above sense. In this paper, we prove that under quite mild conditions, these likelihood functions that result from the application of the theory of structural inference are well-behaved, and possess unique, global maximizers. This research was supported in part by the Applied Mathematical Sciences subprogram of the U.S. Department of Energy under contract W-31-109-Eng-38 while the author was visiting the Mathematics and Computer Science Division of Argonne National Laboratory, Argonne, Illinois.     

Sampling Strategies for Toxic Air Contaminants

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.     

Minority Poverty in Nonmetropolitan Texas*

Abstract Despite a high prevalence of poverty among minorities in nonmetropolitan areas, research and policy concerns regarding poverty have continued focusing on metropolitan minorities. This study uses a model integrating individual, household, and structural factors to examine poverty among Latinos, blacks, and Anglos in nonmetropolitan and, for comparative purposes, metropolitan areas, using data from the 1985 Special Texas Census TDHS 1987. The findings show that minorities in nonmetropolitan areas tend to have the highest poverty rates. In addition, consistent as well as divergent patterns exist among the six ethnic-resident groups with respect to the relationships among the various individual, household, and structural factors and poverty.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

Constrained allocation problems with single-peaked preferences: An axiomatic analysis

We introduce a new class of problems that contains two existing classes: allocation problems with single-peaked preferences and bankruptcy problems. On this class, we analyze the implications of well-known properties such as Pareto optimality, strategy-proofness, resource-monotonicity, no-envy, equal treatment of equals, and two new properties we introduce, hierarchical no-envy and independence of nonbinding constraints. Unlike earlier literature, we consider rules that allow free-disposability. We present characterizations of a rule we introduce on this domain. We relate this rule to well-known rules on the aforementioned subdomains. Based on this relation, we present a characterization of a well-known bankruptcy rule called the constrained equal awards rule. Received: 22 June 2000/Accepted: 21 March 2002 This paper is based on the first chapter of my Ph.D. thesis submitted to the University of Rochester. I wish to thank my advisor, William Thomson, for helpful comments and suggestions.     

Organizational Compatibility and Workplace Drug Testing: Modeling the Adoption of Innovative Social Control Practices

Few researchers have examined organizational variation in the adoption of workplace drug testing, but innovation theory suggests that adoption is more likely when it is compatible with an organization's values, previously introduced ideas, and needs. Using data from the 1997 National Employee Survey, this research models the effects of organizational compatibility, industry, and establishment size on the adoption of drug testing. The data reveal that compatibility, as measured by an organization's rules orientation, presence of an employee assistance program, and mechanization, is associated with the adoption of drug testing. As predicted, the adoption of drug testing varies across industries and by establishment size.     

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467–475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters’ prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters’ prior beliefs.