Approaching in Distribution with Applications to Resampling of Stochastic Processes

We introduce the notion of weak approaching and conditionally weak approaching sequences of random processes. This notion generalizes the conventional weak convergence, and has been proposed for real valued random variables in Belyaev (1995). Some of the standard tools for an investigation of the behaviour of weak approaching sequences of random elements in metric spaces are developed. The spaces of smoothed and right-continuous functions with left-hand limits are considered. This technique allows us to use the resampling approach for an evaluation of distributions of continuous functionals on realizations of sum of an increasing number of independent random processes. Two numerical examples are presented for such functionals as supremum and number of level crossings.     

The intercultural sensitivity of secondary teachers in Hong Kong: a comparative study with implications for professional development

Teacher education programs and teachers’ own lives in the relatively homogeneous communities of the past have hardly equipped them to assist their students to become interculturally sensitive, global citizens. This study compares the levels of intercultural sensitivity of secondary school teachers in four Hong Kong schools using the Intercultural Development Inventory (IDI). Findings indicate unique IDI profiles at each of the four schools in the study and a wide range of IDI scores at each school. Implications of the findings provide the basis for recommendations for the professional development of teachers in these schools.     

The Analysis of Methadone Clinic Data Using Marginal and Conditional Logistic Models with Mixture or Random Effects

The paper develops methods for the statistical analysis of outcomes of methadone maintenance treatment (MMT). Subjects for this study were a cohort of patients entering MMT in Sydney in 1986. Urine drug tests on these subjects were performed weekly during MMT, and were reported as either positive or negative for morphine, the marker of recent heroin use. To allow correlation between the repeated binary measurements, a marginal logistic model was fitted using the generalized estimating equation (GEE) approach and the alternating logistic regression approach. Conditional logistic models are also considered. Results of separate fitting to each patient and score tests suggest that there is substantial between-patient variation in response to MMT. To account for the population heterogeneity and to facilitate subject-specific inference, the conditional logistic model is extended by introducing random intercepts. The two, three and four group mixture models are also investigated. The model of best fit is a three group mixture model, in which about a quarter of the subjects have a poor response to MMT, with continued heroin use independent of daily dose of methadone; about a quarter of the subjects have a very good response, with little or no heroin use, again independent of dose; and about half the subjects responded in a dose-dependent fashion, with reduced heroin use while receiving higher doses of methadone. These findings are consistent with clinical experience. There is also an association between reduced drug use and increased duration in treatment. The mixture model is recommended since it is quite tractable in terms of estimation and model selection as well as being supported by clinical experience.     

A sequential testing procedure for outliers and structural change

In this paper a test for outliers based on externally studentized residuals is shown to be related to a test for predictive failure. The relationships between a test for outliers, a test for a correlated mean shift and a test for an intercept shift are developed. A sequential testing procedure for outliers and structural change is shown to be independent, so that the overall size of the joint test can be determined exactly. It is established that a joint test for outliers and constancy of variances cannot be performed.     

Localizing Combinatorial Properties for Partitions on Block Graphs

We extend the study on partition properties from the set partition to the graph partition, especially for the class of connected block graphs which includes trees. We introduce seventeen partition properties and determine their inter-relations. The notions of k-consistency and k-sortability were studied in the set partition to localize the properties, i.e., a global property can be verified through checking local conditions. We carry on these studies for partitions on connected block graphs. In particular, we completely determine the consistency for all the seventeen properties.     

Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models

Abstract.  Multivariate failure time data arises when each study subject can potentially ex-perience several types of failures or recurrences of a certain phenomenon, or when failure times are sampled in clusters. We formulate the marginal distributions of such multivariate data with semiparametric accelerated failure time models (i.e. linear regression models for log-transformed failure times with arbitrary error distributions) while leaving the dependence structures for related failure times completely unspecified. We develop rank-based monotone estimating functions for the regression parameters of these marginal models based on right-censored observations. The estimating equations can be easily solved via linear programming. The resultant estimators are consistent and asymptotically normal. The limiting covariance matrices can be readily estimated by a novel resampling approach, which does not involve non-parametric density estimation or evaluation of numerical derivatives. The proposed estimators represent consistent roots to the potentially non-monotone estimating equations based on weighted log-rank statistics. Simulation studies show that the new inference procedures perform well in small samples. Illustrations with real medical data are provided.     

A Bayesian compartmental model for the evaluation of 1,3-butadiene metabolism

Summary. We propose a Bayesian model for physiologically based pharmacokinetics of 1,3-butadiene (BD). BD is classified as a suspected human carcinogen and exposure to it is common, especially through cigarette smoke as well as in urban settings. The main aim of the methodology and analysis that are presented here is to quantify variability in the rates of BD metabolism by human subjects. A three-compartmental model is described, together with informative prior distributions for the population parameters, all of which represent real physiological variables. The model is described in detail along with the meanings and interpretations of the associated parameters. A four-compartment model is also given for comparison. Markov chain Monte Carlo methods are described for fitting the model proposed. The model is fitted to toxicokinetic data obtained from 133 healthy subjects (males and females) from the four major racial groups in the USA, with ages ranging from 19 to 62 years. Subjects were exposed to 2 parts per million of BD for 20 min through a face mask by using a computer-controlled exposure and respiratory monitoring system. Stratification by ethnic group results in major changes in the physiological parameters. Sex and age were also tested but not found to have a significant effect.     

Earliness/Tardiness Production Scheduling and Planning,and solutions

Earliness/Tardiness Production Planning (ETPSP) has attracted much attention in recent years. In practice, it provides an efficient way to integrate Manufacturing Resource Planning (MRP-II) Scheduling and with Just-In Time (JIT). Conventional research mainly focused on the condition of single-machine and parallel multi-machine. Capacity balance has not been considered. Some investigations of existing research on ETPSP are given in this paper. An extensive model of ETPSP with consideration of multi-process capacity balance for manufacturing systems is proposed. Two alternative solutions, key-process method and relaxation method, are both developed to solve ETPSP. Computational results identify that both methods are powerful to solve ETPSP which minimizes total earliness and tardiness penalties. Furthermore, some comparisons between these two methods and other conventional methods indicate the efficiency of the former.     

Seven strategies for facilitating access of nontraditional students to graduate education in social work

Undergraduate academic performance as a principal criterion guiding admission to graduate social work education may result in the exclusion of otherwise strong candidates for involvement in graduate education. This paper presents seven strategies for strengthening the admission status of nontraditional students, that is, those students who do not possess adequate undergraduate grade point averages to justify admission. These strategies are particularly important in the United States given the elimination or substantial limitation of affirmative action policies in higher education. Schools of social work, like other educational institutions, must become more creative and proactive to ensure that candidates for graduate education who can make important and substantive contributions to the profession gain entry. Using adult learning theory, the authors offer a rationale that underscores the need to look at an individual's vocational background and professional experience as well as professional commitment to serving vulnerable populations in order to assess readiness for admission. And, the authors identify the importance of offering opportunities to these individuals to strengthen their post-undergraduate academic records in order to be more competitive in the applicant pool. Each of the seven strategies is discussed in terms of its key processes and outcomes in relationship to developing these individuals as viable candidates who can compete in the admission process. The strategies are based on the logic of empowerment theory and they underscore the necessity of building on the strengths and assets that these individuals bring to graduate social work education. The authors illustrate the inclusion of these strategies into the admissions process of a school of social work in the United States and suggest that the use of these strategies can facilitate 'affirmative access' to social work education.     

Positive dependence of random variables with a common marginal distribution

In this paper we review some notions of positive dependence of random variables with a common univariate marginal distribution and describe the related moment and probability inequalities. We first present a comparison between i.i.d. random variables and exchangeable random variables via an application of de Finetti's theorem, then describe some useful probability inequalities via partial orderings of the strength of their positive dependence. Finally, we state a result for random variables which are not necessarily exchangeable. Special applications to the multivariate normal distribution will be discussed, and the results involve only the correlation matrix of the distribution.