Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp-optimization

The conditional tail expectation (CTE) is an indicator of tail behavior that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the median shortfall (MS), although it only gives information about the frequency of a tail event. We construct a class of tail L^p-medians encompassing the MS and CTE. For p in (1,2), a tail L^p-median depends on both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator and another technique to extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on real fire insurance data.     

On a Dualization of Graphical Gaussian Models: A Correction Note

Abstract.  We correct two proofs concerning Markov properties for graphs representing marginal independence relations.     

Weak disintegrability as a form of preservation of coherence

Summary Weak disintegrations are investigated from various points of view. Kolmogorov's definition of conditional probability is critically analysed, and it is noted how the notion of disintegrability plays some role in connecting Kolmogorov's definition with the one given in line with de Finetti's coherence principle. Conditions are given, on the domain of a prevision, implying the equivalence between weak disintegrability and conglomerability. Moreover, weak sintegrations are characterized in terms of coherence, in de Finetti's sense, of, a suitable function. This fact enables us to give, an interpretation of weak disintegrability as a form of “preservation of coherence”. The previous results are also applied to a hypothetical inferential problem. In particular, an inference is shown to be coherent, in the sense of Heath and Sudderth, if and only if a suitable function is coherent, in de Finetti's sense. Research partially supported by: M.U.R.S.T. 40% “Problemi di inferenza pura”.     

Residual analysis for spatial point processes (with discussion)

Summary.  We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity λ plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or co-variate effects. Q – Q -plots of the residuals are effective in diagnosing interpoint interaction.     

论知识经济下复合型外语人才的培养

面对知识经济的挑战,复合型外语人才备受青睐。英语教学必须适应知识经济的新要求,改革现行的考试制度;转变思想观念,更新教育理念;因地制宜,调整课程设置,增设新的教学内容;加强英语教师的培训;制定新的人才培养模式,真抓实干地促进宽口径外语人才的全面发展。     

山西传统民居美学思想初探

从历史、形式与内容、人与自然等三方面对山西传统民居的美学思想做一些探讨     

V＋Rv带宾语的语义框架

以往关于动结式带宾语的研究往往只注意了能否带宾语及其制约因素,但对所带宾语的种类却极少涉及,而这一问题的解决对机器翻译,尤其是同声传译将起到重要的作用。文章认为每个词在其所处的语言系统中占有特定位置,与系统中的某些词具有优先的或固定的组合搭配关系,即每个词都有其默认状态。以当代认知语言学的理论为指导,文章对V Rv能带什么的宾语,它的识别、提取和匹配及推导进行了讨论,得出结论:V对所带宾语提供可能性,面Rv作出限制和选择,也就是说V Rv能带什么样的宾语是有理可据的,其识别和推导是可能的。     

复合词的深层结构和表层结构及其理据性

复合词也有其深层结构和表层结构的区别。从其深层结构向表层结构转化的时候 ,由于音节的制约 ,可能发生结构变形和扭曲现象 ,再加上历史演变的结果 ,仅仅从其表层结构就难以揭示其理据性。对复合词的分析 ,不但不可混淆两种结构 ,还要揭示两种结构之间的联系和区别。     

Missing data and forecasting in multivariate time series: An application of the common components dynamic linear model

Summary The paper deals with missing data and forecasting problems in multivariate time series making use of the Common Components Dynamic Linear Model (DLMCC), presented in Quintana (1985), and West and Harrison (1989). Some results are presented and discussed: exploiting the correlation between series, estimated by the DLMCC, the paper shows as it is possible to update state vector posterior distributions for the unobserved series. This is realized on the base of the updating of the observed series state vectors, for which the usual Kalman filter equations can be applied. An application concerning some Italian private consumption series provides an example of the model capabilities.     

Gini’s nuclear family

The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality.