On simultaneous confidence intervals based on rank-estimates with application to analysis of gene expression data

Abstract

Inferential methods based on ranks present robust and powerful alternative methodology for testing and estimation. In this article, two objectives are followed. First, develop a general method of simultaneous confidence intervals based on the rank estimates of the parameters of a general linear model and derive the asymptotic distribution of the pivotal quantity. Second, extend the method to high dimensional data such as gene expression data for which the usual large sample approximation does not apply. It is common in practice to use the asymptotic distribution to make inference for small samples. The empirical investigation in this article shows that for methods based on the rank-estimates, this approach does not produce a viable inference and should be avoided. A method based on the bootstrap is outlined and it is shown to provide a reliable and accurate method of constructing simultaneous confidence intervals based on rank estimates. In particular it is shown that commonly applied methods of normal or t-approximation are not satisfactory, particularly for large-scale inferences. Methods based on ranks are uniquely suitable for analysis of microarray gene expression data since they often involve large scale inferences based on small samples containing a large number of outliers and violate the assumption of normality. A real microarray data is analyzed using the rank-estimate simultaneous confidence intervals. Viability of the proposed method is assessed through a Monte Carlo simulation study under varied assumptions.     

加德纳多元智力理论对教师教学的意义

在应试教育框架下,人们对智力产生了片面理解:智力=学业智力=语言智力+数理智力。原本丰富多样的多元智力结构被简化为两个方面,对教育实践产生了严重误导。根据加德纳多元智力理论,首先,教师应该摒弃传统的以智力测验和学生学科成绩为标准的评价体系,树立新的学生观、教学观、评价观;其次,要引导学生在多方面智力领域发展,并积极发展优势智力领域;再次,注重培养学生的创造能力,拓宽学生的视野。     

The impact of foster care privatization on multiple placements

The purpose of this study was to assess the impact of foster care privatization policy on multiple placements in Florida's foster care system. A variant of the interrupted time series design allowed for an assessment of privatization policy within 282 data points (six years of data nested in 47 counties). Results from hierarchical linear analysis models identified a significant effect for privatization while controlling for a major alternative explanation. Specifically, the percent of children in fewer than three placements was significantly lower in the post-privatization years than in the pre-privatization years. This effect varied across counties. Line graphs revealed a variety of trends among providers, which may explain the variation of privatization's effect across counties. These results have implications for policymakers seeking to address the goal of permanence and for child welfare administrators involved in the implementation of privatization policy.     

What makes a network go round? Exploring the structure of a strong component with exponential random graph models

A strong component is a subgraph in a directed network where, following the direction of ties, all nodes in the graph are reachable from one another. Mutual reachability implies that every node in the graph is theoretically able to send materials to and/or influence every other node suggesting that strong components are amongst the more egalitarian network structures. Despite this intriguing feature, they remain understudied. Using exponential random graph models (ERGM) for directed networks, we investigate the social and structural processes underlying the generation of strong components. We illustrate our argument using a network of 301 nodes and 703 personal lending ties from Renaissance Florence. ERGM shows that our strong component arises from triadic clustering alongside an absence of higher-order star structures. We contend that these processes produce a strong component with a hierarchical, rather than an egalitarian structure: while some nodes are deeply embedded in a dense network of exchange, the involvement of others is more tenuous. More generally, we argue that such tiered core-periphery strong components will predominate in networks where the social context creates conditions for an absence of preferential attachment alongside the presence of localized closure. Although disparate social processes can give rise to hierarchical strong components linked to these two structural mechanisms, in Florence they are associated with the presence of multiple dimensions of social status and the connectedness of participants across disparate network domains.     

Socio-demographic correlates of multiple causes of death: Real or artifactual?

The socio-demographic and epidemiological correlates of the total number of causes of death (TC) reported on death certificates were examined with multiple classification analysis (MCA). The data were all death certificates on white and black adult residents of Michigan who died at ages 25 or older in 1989 to 1991 (n = 222,763). TC was the sum of every morbid condition named as an underlying, intermediate, or immediate cause of death, or other medical condition contributing to death but not to its underlying cause. Autopsies performed for non-forensic reasons by physicians who are not Medical Examiners (MEs) likely yield the most accurate diagnoses of the underlying medical cause and counts of all other attendant causes, but they are extremely selective of decedents who are most closely integrated into the health care system. Thus we required a socio-demographic pattern in TCs to appear in a multivariate analysis not only for this special group of autopsied decedents but also for the non-autopsied masses before accepting the pattern as real' (not an artifact of underreporting of TC or confoundment with another socio-demographic variable).The MCAs showed that age at death and its underlying medical cause were the most important factors related to TC, as suggested by epidemiologic transition theory. Compared with other underlying causes, diabetes, hypertension, and septicemia yielded the highest average TCs. While sex differences were generally not significant within racial groups, somewhat higher average TCs were found for blacks than whites and for lesser educated than for more educated decedents. These patterns in TC by race and education may reflect lifetime disadvantages faced by blacks and the less educated to health care or information about health practices.     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.     

多元复合认同——以境外俄罗斯人为例

苏联解体后,分布在独联体境内的2500万俄罗斯人,面临民族认同的重新选择现象,新的认同形塑是一个重要问题,“祖国”的消失,心里上的“多元认同”和实体上的“复合身份”,以及该族群的居住国政策和俄罗斯联邦的同胞政策都对其造成影响,多样的认同的存在,不只单是平行的现象,而是一种同一的多层次结构,彼此并不必然会在认同选择的过程中出现冲突。本文试图通过分析这种影响的多重因子,探寻族群属性是否是一种复合体,寻求民族认同的多元复合性。     

在"成功"与"失败"之间--浅谈休闲游戏挑战式的学习方式与电脑辅助教学

CAI不应简单地照搬标准化测试的模式;CAI也不应简单地把传统课本上的内容‘克隆’到电脑上;CAI应当尽量发挥电脑的优势,做出不同于传统教学模式的特色。     

A NEW PROCEDURE FOR ASSESSING LARGE SETS OF CORRELATIONS

In this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices.