Testing homogeneity in discrete mixtures

This paper introduces W-tests for assessing homogeneity in mixtures of discrete probability distributions. A W-test statistic depends on the data solely through parameter estimators and, if a penalized maximum likelihood estimation framework is used, has a tractable asymptotic distribution under the null hypothesis of homogeneity. The large-sample critical values are quantiles of a chi-square distribution multiplied by an estimable constant for which we provide an explicit formula. In particular, the estimation of large-sample critical values does not involve simulation experiments or random field theory. We demonstrate that W-tests are generally competitive with a benchmark test in terms of power to detect heterogeneity. Moreover, in many situations, the large-sample critical values can be used even with small to moderate sample sizes. The main implementation issue (selection of an underlying measure) is thoroughly addressed, and we explain why W-tests are well-suited to problems involving large and online data sets. Application of a W-test is illustrated with an epidemiological data set.     

Prediction intervals for general balanced linear random models

The main interest of prediction intervals lies in the results of a future sample from a previously sampled population. In this article, we develop procedures for the prediction intervals which contain all of a fixed number of future observations for general balanced linear random models. Two methods based on the concept of a generalized pivotal quantity (GPQ) and one based on ANOVA estimators are presented. A simulation study using the balanced one-way random model is conducted to evaluate the proposed methods. It is shown that one of the two GPQ-based and the ANOVA-based methods are computationally more efficient and they also successfully maintain the simulated coverage probabilities close to the nominal confidence level. Hence, they are recommended for practical use. In addition, one example is given to illustrate the applicability of the recommended methods.     

D-optimal designs for logistic models with three and four parameters

Logistic functions are used in different applications, including biological growth studies and assay data analysis. Locally D-optimal designs for logistic models with three and four parameters are investigated. It is shown that these designs are minimally supported. Efficiencies are computed for equally spaced and uniform designs.     

Analysis of one-way layout of count data in the presence of over or under dispersion

This article develops test statistics for the homogeneity of the means of several treatment groups of count data in the presence of over-dispersion or under-dispersion when there is no likelihood available. The C(α)$C(\alpha )$ or score type tests based on the models that are specified by only the first two moments of the counts are obtained using quasi-likelihood, extended quasi-likelihood, and double extended quasi-likelihood. Monte Carlo simulations are then used to study the comparative behavior of these C(α)$C(\alpha )$ statistics compared to the C(α)$C(\alpha )$ statistic based on a parametric model, namely, the negative binomial model, in terms of the following: size; power; robustness for departures from the data distribution as well as dispersion homogeneity. These simulations demonstrate that the C(α)$C(\alpha )$ statistic based on the double extended quasi-likelihood holds the nominal size at the 5% level well in all data situations, and it shows some edge in power over the other statistics, and, in particular, it performs much better than the commonly used statistic based on the quasi-likelihood. This C(α)$C(\alpha )$ statistic also shows robustness for moderate heterogeneity due to dispersion. Finally, applications to ecological, toxicological and biological data are given.     

Adventures in policy modeling! Operations research in the community and beyond

The literature describing operations research in the community is somewhat of a puzzle. On the one hand, several authors have denigrated the use of traditional operations approaches in addressing community problems, yet several studies document successful applications. Arguing that the operations research mindset is itself a great strength, we will review several examples where operations research methods have been employed creatively to the benefit of the community and beyond.     

分层教学在职业学校数学教学中的应用探索

为了更好地提高职业学校数学课的教学质量,针对传统数学教学模式在目前教学中出现的诸多问题,我们在职业学校数学教学中采用＂分层次＂的教学法进行实验和研究,结果发现,＂分层次＂教学法不仅有利于提高学生学习的积极性、主动性和创造性,有利于培养学生学习兴趣和自我锻炼能力,有利于学生比较牢固地掌握知识和技能,同时,这种方法还为学生终身学习奠定了良好的基础。     

贺兰山高等真菌区系地理研究

贺兰山高等真菌区系地理成分中,世界性分布属占64.1%、种占19.5,他们多为适应性强的腐生菌类;欧亚北美分布属占35.9%、种占52.7%,未发现热带分布的属或种,充分显示出该地区真菌以北温带分布成分为主的特点;欧亚分布种占11.5%,东亚北美分布种占9.9%,表明该地区真菌区系与欧洲、北美洲的密切联系;中国&日本分布种占3.1%,可见本地区和日本在真菌区系上也有着联系;本地区特有成分较少,但从贺兰山特殊的地理位置、相对孤立的山体和复杂的地形分析,随研究工作的深入,很可能有一些山的分布的特有成分被发现.贺兰山真菌区系成分与邻近的内蒙古大青山相比较,共有种多达57种,而与地处亚热带向热带过渡的湖南莽山相比较,共有种仅有12种,更进一步说明本地区深居北温带,真菌区系以泛北极成分为主的特色.     

课外补习、贫富差距的映像与代际变化

本文以武汉市L小学和M大学的调查为基础,说明课外补习与贫富差距之间的联系。各种形式和内容的课外补习既是城乡差距和贫富差距的具体映像,也是维持和推动社会贫富差距的重要力量,使得这一差距具有代际传递特征。在人们越来越关注学校教育公平的今天,课外补习对贫富差距的形成与扩大的消极作用却被忽视;但它所起的维持和传递作用在将来会更大、更顽固。因此。政府要将课外补习限制在一定范围内,并改革正规学校教育系统及人才评估与选拔机制．尽可能地消减这一市场活动的负面作用。     

Selecting and checking a binomial response generalized linear model using phi-divergences

This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is considered. Diagnostic methods based on divergence measures such as a new measure to detect leverage points and two indicators to detect influential points are introduced. As an illustration, the diagnostics are applied to human psychology data.