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.     

社会学视野中的教育及民族教育

社会学对于教育和民族教育问题的研究更为看重对教育得以运行的社会宏观背景的关注。从社会学的学科视野出发,作为培养人的一种社会活动和一种社会设置,教育无时无刻表征着社会生活的现实,所以,教育就应该凸显它本来就具有的社会底蕴;而社会学视野中的民族教育,自有其更为宽广的社会背景、更为深厚的学术支撑和更为丰富的学理内涵,本文就此展开了论述。     

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.     

Regression models to dependence for exceedance

Extreme Value Theory (EVT) aims to study the tails of probability distributions in order to measure and quantify extreme events of maximum and minimum. In river flow data, an extreme level of a river may be related to the level of a neighboring river that flows into it. In this type of data, it is very common for flooding of a location to have been caused by a very large flow from an affluent river that is tens or hundreds of kilometers from this location. In this sense, an interesting approach is to consider a conditional model for the estimation of a multivariate model. Inspired by this idea, we propose a Bayesian model to describe the dependence of exceedance between rivers, where we considered a conditionally independent structure. In this model, the dependence between rivers is captured by modeling the excess marginally of one river as a consequence of linear functions of the other rivers. The results showed that there is a strong and positive connection between excesses in one river caused by the excesses of the other rivers.     

Kernel density estimation under negative superadditive dependence and its application for real data

In this paper, the kernel density estimator for negatively superadditive dependent random variables is studied. The exponential inequalities and the exponential rate for the kernel estimator of density function with a uniform version, over compact sets are investigated. Also, the optimal bandwidth rate of the estimator is obtained using mean integrated squared error. The results are generalized and used to improve the ones obtained for the case of associated sequences. As an application, FGM sequences that fulfil our assumptions are investigated. Also, the convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.     

Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

辽宁部分高中田径选项课的现状及发展对策

采用问卷调查、专家访谈、文献资料等方法,对辽宁省重点、普通中学高中开设田径选项课的现状进行了调查分析.研究发现,当前辽宁省重点、普通高中田径选项课正面临困境.究其原因,主要是教师对田径选项课的价值认识不足;此外,当前的田径选项课缺乏趣味性,使学生产生厌学情绪.结合健康体育教育及终身体育教育,对田径选项课在中学体育课中的地位与作用进行了论述,并针对中学田径选项课的发展提出积极的对策和建议;同时,为解决高校田径选项课中的问题提供了参考与借鉴.     

循化撒拉族村落名称考释

本文对循化县撒拉族村落的名称及含义进行了调查并作了初步的分析 ,村落名称反映了一个社会群体的历史沿革、居处环境以及人文精神和美学追求。通过本文的探讨 ,祈望引起更多学者对撒拉族社会群体的关注。     

A framework for the comparison of maximum pseudo-likelihood and maximum likelihood estimation of exponential family random graph models

The statistical modeling of social network data is difficult due to the complex dependence structure of the tie variables. Statistical exponential families of distributions provide a flexible way to model such dependence. They enable the statistical characteristics of the network to be encapsulated within an exponential family random graph (ERG) model. For a long time, however, likelihood-based estimation was only feasible for ERG models assuming dyad independence. For more realistic and complex models inference has been based on the pseudo-likelihood. Recent advances in computational methods have made likelihood-based inference practical, and comparison of the different estimators possible.