Elementary renewal theorems for widely dependent random variables with applications to precise large deviations

Abstract

On the basis of Wang and Cheng (J. Math. Anal. Appl. 384 (2011) 597–606), this paper further investigates elementary renewal theorems for counting processes generated by random walks with widely orthant dependent increments. The obtained results improve the corresponding ones of the above-mentioned paper mainly in the sense of weakening the moment conditions on the positive parts of the increments. Meanwhile, a revised version of strong law of large numbers for random walks with widely orthant dependent increments is established, which improves Theorem 1.4 of Wang and Cheng (2011 Wang, Y., and D. Cheng. 2011. Basic renewal theorems for a random walk with widely dependent increments and their applications. Journal of Mathematical Analysis and Applications 384 (2):597–606. doi:10.1016/j.jmaa.2011.06.010.[Crossref], [Web of Science ®] , [Google Scholar]) by enlarging the regions of dominating coefficients. Finally, by using the above results, some precise large deviation results for a nonstandard renewal risk model are established, in which the innovations are widely orthant dependent random variables with common heavy tails, and the inter-arrival times are also widely orthant dependent.     

《孟子》释读辨误(四则)

传统经典须细读，在细读的基础上领会真义。历代注家对《孟子》的注疏多有误读之处，如"攘"，本义为"取自来之物"，经"多少同盗"，演变为"攘"即"盗"；"巨室"初谓国君住的大房子，这里当喻指国君，但注家多强解为指大臣；舜在"完廪""浚井"的过程中是如何脱难的，本文没有说，注家依据其他材料做了合理化解读，未必符合本义。"坏宫室以为汙池"，如从人类社会发展史的角度来释读，实际上是要维持以渔猎为生的生存方式。致误的根源有"非黑即白"的思维方式、前后矛盾、对古代"不雅驯"的文字进行改造等。     

Orientation relationship in finite dimensional space

In the present article, we discuss the regression of a point on the surface of a unit sphere in d dimensions given a point on the surface of a unit sphere in p dimensions, where p may not be equal to d. Point projection is added to the rotation and linear transformation for regression link function. The identifiability of the model is proved. Then, parameter estimation in this set up is discussed. Simulation studies and data analyses are done to illustrate the model.     

A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

浅埋大跨黄土隧道下穿公路方案比选

以大跨黄土隧道下穿公路安全施工为背景,对隧道下穿公路的安全施工方案进行研究。基于公路路面破损指数与下穿公路施工风险事件引起路面最大沉降之间的关系确定了隧道下穿施工可能引起的路面最大允许沉降量,并据此制定出施工管理基准,对比分析了CRD和CD法引起的隧道拱顶沉降、地表最大沉降、支护受力和隧道周边地层塑性区特征,建议采用CD法进行下穿施工。下穿孙辛路施工监测结果表明,采用CD法保证了隧道施工安全和孙辛路的正常通行。     

团队反思对员工绩效影响的跨层次研究

通过建立跨层次的中介效应模型,运用多层线性模型方法,考察团队反思对员工绩效的影响。选取交互记忆系统和团队绩效两个中介变量,基于86个企业团队的数据进行实证研究,指出团队反思对员工绩效存在跨层次的影响,并且在此影响机制中交互记忆系统起到了中介作用,但团队绩效对员工绩效的直接影响效应不显著,即团队绩效对员工绩效无明显促进作用。     

大型音乐舞蹈史诗《中国革命之歌》的艺术处理

大型音乐舞蹈史诗《中国革命之歌》在进行创作时既要确保艺术创作真实反映历史事实,又要防止与《东方红》重复,需要创作人员精心设计框架,选择材料进行加工改编,具有一定的难度。创作者和表演者通过艺术框架的搭建、艺术素材的加工、艺术演出的处理,使大型音乐舞蹈史诗《中国革命之歌》既具有政治内容又具有极高的艺术美。     

Testing Serial Correlation in Partially Linear Additive Errors-in-variables Models

This article considers testing serial correlation in partially linear additive errors-in-variables model. Based on the empirical likelihood based approach, a test statistic was proposed, and it was shown to follow asymptotically a chi-square distribution under the null hypothesis of no serial correlation. Finally, some simulation studies are conducted to illustrate the performance of the proposed method.