Two-moment approximations to some null distributions in order-restricted inference: Unequal sample sizes

Bartholomew's statistics for testing homogeneity of normal means with ordered alternatives have null distributions which are mixtures of chi-squared or beta distributions according as the variances are known or not. If the sample sizes are not equal, the mixing coefficients can be difficult to compute. For a simple order and a simple tree ordering, approximations to the significance levels of these tests have been developed which are based on patterns in the weight sets. However, for a moderate or large number of means, these approximations can be tedious to implement. Employing the same approach that was used in the development of these approximations, two-moment chisquared and beta approximations are derived for these significance levels. Approximations are also developed for the testing situation in which the order restriction is the null hypothesis. Numerical studies show that in each of the cases the two-moment approximation is quite satisfactory for most practical purposes.     

Simplified Containment Event Tree Methodology Applied to Peach Bottom SBO-ST Sequences1

The methodology presented here identifies an approach to accurately and economically analyze the effects on risk of various containment performance issues. Although this method facilitates the evaluation of potential containment improvements, it does so while utilizing the significant amount of information accumulated by the U.S. NRC Reactor Risk Reference Program. The use of hindsight and the acceptance of point estimate quantifications of risks allows the proposed methodology to be scrutable and understandable to the community as well as relatively simple and inexpensive to apply. A study of containment venting strategies was used to demonstrate the capabilities of the simplified containment event tree methodology. However, the methodology is flexible enough for a wide range of risk evaluations.     

Robust automatic methods for outlier and error detection

Summary.  Editing in surveys of economic populations is often complicated by the fact that outliers due to errors in the data are mixed in with correct, but extreme, data values. We describe and evaluate two automatic techniques for the identification of errors in such long-tailed data distributions. The first is a forward search procedure based on finding a sequence of error-free subsets of the error-contaminated data and then using regression modelling within these subsets to identify errors. The second uses a robust regression tree modelling procedure to identify errors. Both approaches can be implemented on a univariate basis or on a multivariate basis. An application to a business survey data set that contains a mix of extreme errors and true outliers is described.     

The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree

This article is devoted to the strong law of large numbers and the entropy ergodic theorem for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree, which generalizes the relevant results of tree-indexed nonhomogeneous bifurcating Markov chains. Meanwhile, our proof is quite different from the traditional method.     

D s -optimal designs for Kozak's tree taper model

In this work, we study D _s -optimal design for Kozak's tree taper model. The approximate D _s -optimal designs are found invariant to tree size and hence create a ground to construct a general replication-free D _s -optimal design. Even though the designs are found not to be dependent on the parameter value p of the Kozak's model, they are sensitive to the s×1 subset parameter vector values of the model. The 12 points replication-free design (with 91% efficiency) suggested in this study is believed to reduce cost and time for data collection and more importantly to precisely estimate the subset parameters of interest.     

Selection without (unfair) discrimination

A method is devised for performing multiple discriminant analysis subject to inequality constraints on the probabilities of misassignment of different subpopulations. This procedure is motivated by attempts to devise.fair means of selection of applicants for schools, jobs, and credit. An algorithm is developed and sample calculations are given.     

A Distribution-free Multivariate Change-point Model for Statistical Process Control

This article develops a new distribution-free multivariate procedure for statistical process control based on minimal spanning tree (MST), which integrates a multivariate two-sample goodness-of-fit (GOF) test based on MST and change-point model. Simulation results show that our proposed procedure is quite robust to nonnormally distributed data, and moreover, it is efficient in detecting process shifts, especially moderate to large shifts, which is one of the main drawbacks of most distribution-free procedures in the literature. The proposed procedure is particularly useful in start-up situations. Comparison results and a real data example show that our proposed procedure has great potential for application.     

A Meta‐Analysis of Carbon Nanotube Pulmonary Toxicity Studies—How Physical Dimensions and Impurities Affect the Toxicity of Carbon Nanotubes

This article presents a regression‐tree‐based meta‐analysis of rodent pulmonary toxicity studies of uncoated, nonfunctionalized carbon nanotube (CNT) exposure. The resulting analysis provides quantitative estimates of the contribution of CNT attributes (impurities, physical dimensions, and aggregation) to pulmonary toxicity indicators in bronchoalveolar lavage fluid: neutrophil and macrophage count, and lactate dehydrogenase and total protein concentrations. The method employs classification and regression tree (CART) models, techniques that are relatively insensitive to data defects that impair other types of regression analysis: high dimensionality, nonlinearity, correlated variables, and significant quantities of missing values. Three types of analysis are presented: the RT, the random forest (RF), and a random‐forest‐based dose‐response model. The RT shows the best single model supported by all the data and typically contains a small number of variables. The RF shows how much variance reduction is associated with every variable in the data set. The dose‐response model is used to isolate the effects of CNT attributes from the CNT dose, showing the shift in the dose‐response caused by the attribute across the measured range of CNT doses. It was found that the CNT attributes that contribute the most to pulmonary toxicity were metallic impurities (cobalt significantly increased observed toxicity, while other impurities had mixed effects), CNT length (negatively correlated with most toxicity indicators), CNT diameter (significantly positively associated with toxicity), and aggregate size (negatively correlated with cell damage indicators and positively correlated with immune response indicators). Increasing CNT N₂‐BET‐specific surface area decreased toxicity indicators.     

南亚树木崇拜和佛经母题对于树神传说的触媒

三国两晋时代,南亚树木崇拜传入流播,与中土生态困境引发的理性思考交汇,构成了中土民俗心态的一次震撼。其在介乎民俗传说和文学之间的树神母题中,凄楚而顽强地表现出来。佛经故事母题伴随着佛教的众生平等、戒禁杀生等观念,深入到中国古人民俗心理中。树神崇拜也成为中国古代植物神崇拜的核心。     

小微企业众筹融资平台风险管理研究

小微企业作为经济发展的重要力量,在发展过程中面临融资难、融资贵等问题,众筹融资作为新兴的网络融资模式不仅给小微企业带来了机遇,也带来了挑战。对小微企业众筹融资整体风险进行识别,提出“5+11”风险识别途径,着重研究众筹融资平台面临的风险,利用系统动力学方法绘制小微企业众筹融资平台风险系统的因果关系图,并根据因果关系图形成回路图和原因树,更直观地展现众筹融资平台风险的反馈作用机制。针对风险提出相应的防范对策,对规范众筹融资平台运作、提高平台融资成功率具有一定的实际意义。