Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands

The mean and variance of a sum of a random number of random variables are well known when the number of summands is independent of each summand and when the summands are independent and identically distributed (iid), or when all summands are identical. In scientific and financial applications, the preceding conditions are often too restrictive. Here, we calculate the mean and variance of a sum of a random number of random summands when the mean and variance of each summand depend on the number of summands and when every pair of summands has the same correlation. This article shows that the variance increases with the correlation between summands and equals the variance in the iid or identical cases when the correlation is zero or one.     

从题材演变看“游龙戏凤”故事主题的变迁及意义

在游龙戏凤故事的发展过程中,话本小说《客窗闲话》与杂剧《梅龙镇》和电影《龙凤店》,是非常重要的三部作品,这三部作品虽然围绕皇帝微服出游展开想象,但是在内容上还是有差异的,这就导致了主题相应地发生变化。《客窗闲话》突出原道说教意义,强调＂戒色＂;《梅龙镇》描写充满神性的皇帝的情欲追求;《龙凤店》则展示了人性的力量。     

“乱写”的性情之文——废名散文美学风格

散文是理解文学家和哲学家废名的桥梁,是其创作整体性研究中不可或缺的一环。其散文以＂隔＂为特色,一定程度上造成研究难度,但可从废名和周作人师生之间＂隔＂的异同,窥其一脉相承的文学趣味。从散文形式上剖析,废名从六朝散文中提炼出＂乱写＂的观念,其实质是重灵感的创作心理。二者共同形成其散文独特的＂乱写＂之＂隔＂的美学风格,有助于理解废名后期创作走向。     

浅析寻衅滋事罪中的“随意殴打他人”——从肖传国案说起

寻衅滋事罪是从1979年刑法中的流氓罪分解独立形成的一个罪名,也是司法实践中较难以认定的罪名之一。对于随意殴打他人的寻衅滋事行为理解不应该仅局限于主观因素,应当从行为人殴打的动机、殴打的时间和地点、殴打的对象、殴打的方式等主客观结合综合考虑,并从这些方面区分与故意伤害行为。肖传国等人的行为是故意伤害行为,而非寻衅滋事行为。     

Dissolution risks in first and higher order marital and cohabiting unions

More and more people enter multiple unions during their lives, and then they may choose to either cohabit or marry. We examine the implications of this diversity in partnership trajectories by assessing dissolution risks in first and higher order marital and cohabiting unions. We use recent Norwegian survey data that contain complete retrospective union histories. We find that, when selectivity is accounted for, higher-order unions are not less stable than first unions. When dissolution risks for all possible partnership trajectories are compared, we find that former cohabitants who cohabit in a second union are as likely to break up as they were in their first cohabiting union. As soon as they enter marriage in their second unions, however, they do slightly better than first married persons. The previously married experience higher dissolution risks in their second union compared to their first, regardless of their current union type.     

Distribution of the C statistic with applications to the sample mean of Poisson data

The C statistic, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. The main advantage of this statistic, compared to the more commonly used χ2 statistic, is its applicability without the need to combine data points. This feature has made the C statistic a very useful method to analyze Poisson data that have small (or even null) counts in each resolution element. One of the challenges of the C statistic is that its probability distribution, under the null hypothesis that the data follow a parent model, is not known exactly. This paper presents an effort towards improving our understanding of the C statistic by studying (a) the distribution of C statistic for a fully specified model, (b) the distribution of C_min resulting from a maximum-likelihood fit to a simple one-parameter constant model, i.e. a model that represents the sample mean of N Poisson measurements, and (c) the distribution of the associated ΔC statistic that is used for parameter estimation. The results confirm the expectation that, in the high-count limit, both C statistic and C_min have the same mean and variance as a χ2 statistic with same number of degrees of freedom. It is also found that, in the low-count regime, the expectation of the C statistic and C_min can be substantially lower than for a χ2 distribution. The paper makes use of recent X-ray observations of the astronomical source PG 1116+215 to illustrate the application of the C statistic to Poisson data.     

开征环境税对经济增长影响的实证研究——基于十二个发达国家二氧化碳税开征经验的面板数据分析

本文利用芬兰等十二个已开征二氧化碳税的发达国家1980～2009年间的跨国面板数据进行随机效应估计.结果发现:开征环境税在短期内可能给经济增长带来负向冲击;但环境税对经济增长的影响更多地体现为长期冲击,且这种长期冲击是显著的负向影响.因此,开征环境税时,不仅要通过税收体系调整缓解企业成本上升在短期内给经济增长带来的不利冲击,更应从长期影响的视角出发,设计配套政策,降低环境税在长期内对经济增长和社会福利可能存在的不利影响.     

The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines

In designed experiments and in particular longitudinal studies, the aim may be to assess the effect of a quantitative variable such as time on treatment effects. Modelling treatment effects can be complex in the presence of other sources of variation. Three examples are presented to illustrate an approach to analysis in such cases. The first example is a longitudinal experiment on the growth of cows under a factorial treatment structure where serial correlation and variance heterogeneity complicate the analysis. The second example involves the calibration of optical density and the concentration of a protein DNase in the presence of sampling variation and variance heterogeneity. The final example is a multienvironment agricultural field experiment in which a yield–seeding rate relationship is required for several varieties of lupins. Spatial variation within environments, heterogeneity between environments and variation between varieties all need to be incorporated in the analysis. In this paper, the cubic smoothing spline is used in conjunction with fixed and random effects, random coefficients and variance modelling to provide simultaneous modelling of trends and covariance structure. The key result that allows coherent and flexible empirical model building in complex situations is the linear mixed model representation of the cubic smoothing spline. An extension is proposed in which trend is partitioned into smooth and non-smooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented.     

A comparison of population average and random-effect models for the analysis of longitudinal count data with base-line information

The generalized estimating equation (GEE) approach to the analysis of longitudinal data has many attractive robustness properties and can provide a 'population average' characterization of interest, for example, to clinicians who have to treat patients on the basis of their observed characteristics. However, these methods have limitations which restrict their usefulness in both the social and the medical sciences. This conclusion is based on the premise that the main motivations for longitudinal analysis are insight into microlevel dynamics and improved control for omitted or unmeasured variables. We claim that to address these issues a properly formulated random-effects model is required. In addition to a theoretical assessment of some of the issues, we illustrate this by reanalysing data on polyp counts. In this example, the covariates include a base-line outcome, and the effectiveness of the treatment seems to vary by base-line. We compare the random-effects approach with the GEE approach and conclude that the GEE approach is inappropriate for assessing the treatment effects for these data.     

Weight matrices for social influence analysis: An investigation of measurement errors and their effect on model identification and estimation quality

Weight matrices, such as used in network autocorrelation models, are useful to investigate social influence processes. The objective of this paper is to investigate a key topic that has received relatively little attention in previous research, namely the issues that arise when observational limitations lead to measurement errors in these weight matrices. Measurement errors are investigated from two perspectives: when relevant ties are omitted, and when irrelevant ties are erroneously included as part of the matrix. The paper first shows analytically that these two situations result in biased estimates. Next, a simulation experiment provides evidence of the effect of erroneously coding the weight matrix on model performance and the ability of a network autocorrelation test to identify social influence effects. The results suggest that depending on the level of autocorrelation and the topology attributes of the underlying matrix, there is a window of opportunity to identify and model social influence processes even in situations where the ties in a matrix cannot be accurately observed.