A note on the satterthwaite confidence interval for a variance

When using a Satterthwaite chi-squared approximation, it is generally thought that the approximation is satisfactory when it is applied to a positive linear combination of mean squares. In this note, we describe how the Williams - Tukey idea for getting a confidence interval for the among groups variance in a random one-way model can be incorporated into Satterthwaite’s procedure for getting a confidence interval for a variance. This adjusted Satterthwaite procedure insures that his chi-squared approximation is always applied to positive linear combinations of mean squares. A small simulation is included which suggests that the adjustment to the Satterthwaite procedure is effective.     

A Bayes comparison of Weibull extension and modified Weibull models for data showing bathtub hazard rate

A number of models have been proposed in the literature to model data reflecting bathtub-shaped hazard rate functions. Mixture distributions provide the obvious choice for modelling such data sets but these contain too many parameters and hamper the accuracy of the inferential procedures particularly when the data are meagre. Recently, a few distributions have been proposed which are simply generalizations of the two-parameter Weibull model and are capable of producing bathtub behaviour of the hazard rate function. The Weibull extension and the modified Weibull models are two such families. This study focuses on comparing these two distributions for data sets exhibiting bathtub shape of the hazard rate. Bayesian tools are preferred due to their wide range of applicability in various nested and non-nested model comparison problems. Real data illustrations are provided so that a particular model can be recommended based on various tools of model comparison discussed in the paper.     

Reliability estimation in stress–strength models: an MCMC approach

In this paper, we consider the estimation of the stress–strength parameter R=P(Y<X) when X and Y are independent and both are modified Weibull distributions with the common two shape parameters but different scale parameters. The Markov Chain Monte Carlo sampling method is used for posterior inference of the reliability of the stress–strength model. The maximum-likelihood estimator of R and its asymptotic distribution are obtained. Based on the asymptotic distribution, the confidence interval of R can be obtained using the delta method. We also propose a bootstrap confidence interval of R. The Bayesian estimators with balanced loss function, using informative and non-informative priors, are derived. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations.     

Estimation of the Proportion of Defective Units by Using Group Testing Under the Existence of a Threshold of Detection

Group testing procedures, in which groups containing several units are tested without testing each unit, are widely used as cost-effective procedures in estimating the proportion of defective units in a population. A problem arises when we apply these procedures to the detection of genetically modified organisms (GMOs), because the analytical instrument for detecting GMOs has a threshold of detection. If the group size (i.e., the number of units within a group) is large, the GMOs in a group are not detected due to the dilution even if the group contains one unit of GMOs. Thus, most people conventionally use a small group size (which we call conventional group size) so that they can surely detect the existence of defective units if at least one unit of GMOs is included in the group. However, we show that we can estimate the proportion of defective units for any group size even if a threshold of detection exists; the estimate of the proportion of defective units is easily obtained by using functions implemented in a spreadsheet. Then, we show that the conventional group size is not always optimal in controlling a consumer's risk, because such a group size requires a larger number of groups for testing.     

Tests for homogeneity of risk differences in stratified design with correlated bilateral data

ABSTRACT

Correlated bilateral data arise from stratified studies involving paired body organs in a subject. When it is desirable to conduct inference on the scale of risk difference, one needs first to assess the assumption of homogeneity in risk differences across strata. For testing homogeneity of risk differences, we herein propose eight methods derived respectively from weighted-least-squares (WLS), the Mantel-Haenszel (MH) estimator, the WLS method in combination with inverse hyperbolic tangent transformation, and the test statistics based on their log-transformation, the modified Score test statistic and Likelihood ratio test statistic. Simulation results showed that four of the tests perform well in general, with the tests based on the WLS method and inverse hyperbolic tangent transformation always performing satisfactorily even under small sample size designs. The methods are illustrated with a dataset.     

Understanding public perceptions of genetically modified organisms in China: The role that heuristics play during digital media exposure

This study explicates the role that heuristics play in influencing Chinese public perceptions of genetically modified organisms (GMO) when they are exposed to digital media. According to the cognitive–affective continuum of heuristics, trust in scientists and negative emotions about GMOs are a cognition-oriented heuristic and an affect heuristic, respectively. The statistical results of an online survey (N?=?414) demonstrated that trust in scientists fully mediated digital media exposure and perceptions of the risks versus benefits of GMOs. In addition, negative emotions moderated the full mediation effect, showing that the indirect effect was stronger in individuals with low levels of negative emotions than in those with high levels of negative emotions. The mediating role of trust in scientists and the moderating role of negative emotions, the two heuristics applied in this study, indicated that when negative emotions were weak, laypeople were more likely to rely on scientists to judge the consequences of GMOs than systematically process the associated information by themselves. The findings have implications for reconsidering the importance of heuristic processing in building reasonable public perceptions of risk-laden technologies through the digital environment.     

两类含两个变态贝塞尔函数积的积分公式

从变态贝塞尔方程出发,构造了它的一个变换形式,利用微积分学中的定理,巧妙地求得了含两个变态贝塞尔函数和的积的一个普遍的积分公式。进而利用变态贝塞尔函数的性质,可简洁地推导出电磁场领域中两类非常重要的积分的解析表达式,在处理圆柱结构下有关电磁场能量或电磁波传输功率的计算问题时,具有普遍的应用价值。     

Inference in Censored Models with Endogenous Regressors

This paper analyzes the linear regression model y = xβ+ε with a conditional median assumption med (ε| z) = 0, where z is a vector of exogenous instrument random variables. We study inference on the parameter β when y is censored and x is endogenous. We treat the censored model as a model with interval observation on an outcome, thus obtaining an incomplete model with inequality restrictions on conditional median regressions. We analyze the identified features of the model and provide sufficient conditions for point identification of the parameter β. We use a minimum distance estimator to consistently estimate the identified features of the model. We show that under point identification conditions and additional regularity conditions, the estimator based on inequality restrictions is normal and we derive its asymptotic variance. One can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring. A Monte Carlo analysis illustrates our estimator in the censored and the uncensored case.     

“农业科技创新与服务”笔谈：依托科技创新与服务加快油菜产业发展方式转变

基于农业科技创新与服务是现代农业发展的重要支撑,本刊延请中国工程院官春云院士就如何依托农业科技创新与服务加快我国油菜产业发展方式转变,湖南农大科技督导团专家就转基因农作物研发,湖南省委农村工作部董成森先生就当前农业科技创新面临的问题与对策展开笔谈。官春云院士在分析我国油菜产业存在的主要问题基础上,提出要通过选育和推广油菜新品种,大力推行标准化栽培,狠抓油菜产品的精深加工,以促进油菜产业发展方式的转变。湖南农大科技督导团基于国内外转基因农作物研究的发展态势和对湖南农大的考察,认为湖南乃至全国在主要农艺性状基因发掘和功能研究、分子设计育种理论研究、完全自主知识产权的基因研究等方面存在不足,要抓住“十二五”关键时期,加强顶层设计,明确发展规划和战略重点,加大高端人才培养、引进和经费投入力度,加快植物分子设计育种研究,以尽可能抢占转基因技术研究制高点,同时高度重视转基因植物生物安全问题。董成森先生以湖南为例分析了当前农业科技创新与服务中存在的主要问题,并从树立新的农业科技观,整合农业科研资源,增加农业科技投入,培养和引进农业科技精英人才,提高农业科技成果的转化率提出了相关对策。