Limit theorems for dependent Bernoulli variables with statistical inference

We consider a class of dependent Bernoulli variables where the conditional success probability is a linear combination of the last few trials and the original success probability. We obtain its limit theorems including the strong law of large numbers, weak invariance principle, and law of the iterated logarithm. We also derive some statistical inference results which make the model applicable. Simulation results are exhibited as well to show that with small sample size the convergence rate is satisfying and the proposed estimators behave well.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

In this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984 Bierens, H. J. (1984). Model specification testing of time series regressions. Journal of Econometrics 26:323–353.[Crossref], [Web of Science ®] , [Google Scholar]) for time series regression models with the simulated ICM test of Bierens and Wang (2012 Bierens, H. J., Wang, L. (2012). Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28:328–362.[Crossref], [Web of Science ®] , [Google Scholar]) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.     

Varying kernel marginal density estimator for a positive time series

This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel.     

Some novel results on pairwise quasi-asymptotical independence with applications to risk theory

In this article we obtain some novel results on pairwise quasi-asymptotically independent (pQAI) random variables. Concretely speaking, let X₁, …, X_n be n real-valued pQAI random variables, and W₁, …, W_n be another n non negative and arbitrarily dependent random variables, but independent of X₁, …, X_n. Under some mild conditions, we prove that W₁X₁, …, W_nX_n are still pQAI as well. Our result is in a general setting whether the primary random variables X₁, …, X_n are heavy-tailed or not. Finally, a special case of above result is applied to risk theory for investigating the finite-time ruin probability for a discrete-time risk model with a wide type of dependence structure.     

An efficient and fast algorithm for estimating the frequencies of superimposed exponential signals in zero-mean multiplicative and additive noise

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains O _p (N ^?3/2), which is the best convergence rate in the case of only additive noise and constant amplitude.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.     

德川时代日本儒者对孔子“吾道一以贯之”的诠释——东亚比较思想史的视野

德川时代日本儒者对“吾道一以贯之”解释的主要观点是 :多数日本儒者将孔子的“道”界定为社会政治意义的“道”,是经世济民之道。对“一以贯之”的解释要点是 :“贯 ,统也”;以“仁”释“一”;从伊藤仁斋开始 ,德川时代儒者对上述命题的解释 ,部分地体现日本儒者采取“即存在论本质”的解经方法 ,呈现极其强烈的反宋学思想倾向 ,尤其以朱子学为主要攻击目标。韩儒对上述命题的解释 ,则因袭多于创新。从中日比较思想史视野来看 ,日本儒者对宋学的批判并未切中要害 ,因为他们并未进入宋儒之孔学诠释中的两个哲学问题 ,这就是“心与理之关系”以及“个体论或整体论之方法论问题”。     

分布时滞Hopfield神经网络稳定性

针对分布时滞的Hopfield型神经网络构造了李雅普诺夫能量函数,证明了该网络的稳定性问题。证明过程中运用了引理的结论,充分利用了所取李雅普诺夫函数的特殊性,较多地运用了不等式分析方法及不等式放缩技巧。同时由于时滞的存在,证明过程中还涉及李雅普诺夫泛函问题。最后利用引理的结论得出了该网络全局一致渐近稳定的结论。     

大学后继续教育问题探讨

大学后继续教育,是一种高层次的成人教育,在世界各国社会经济的发展中,发挥着极其重要的智力支持和人才贡献作用。深刻认识大学后继续教育的科学内涵,切实把握大学后继续教育的特征与功能,对于促进大学后继续教育的发展,推动我国全面建设小康社会目标的实现,具有十分重要的意义。