A detection algorithm for the first jump time in sample trajectories of jump-diffusions driven by α-stable white noise

Abstract

The purpose of this paper is to develop a detection algorithm for the first jump point in sampling trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by α-stable white noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilize computer simulation algorithm in MATLAB to visualize the sampling trajectories of the jump-diffusions for various combinations of parameters arising in the modeling structure of stochastic differential equations.     

Variable Selection in Joint Location and Scale Models of the Skew-t-Normal Distribution

Variable selection is an important issue in all regression analysis, and in this article, we investigate the simultaneous variable selection in joint location and scale models of the skew-t-normal distribution when the dataset under consideration involves heavy tail and asymmetric outcomes. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. These estimators are compared by simulation studies.     

Zone control charts with estimated parameters for detecting prespecified changes in linear profiles

ABSTRACT

In profile monitoring, control charts are proposed to detect unanticipated changes, and it is usually assumed that the in-control parameters are known. However, due to the characteristics of a system or process, the prespecified changes would appear in the process. Moreover, in most applications, the in-control parameters are usually unknown. To overcome these issues, we develop the zone control charts with estimated parameters to detect small shifts of these prespecified changes. The effects of estimation error have been investigated on the performance of the proposed charts. To account for the practitioner-to-practitioner variability, the expected average run length (ARL) and the standard deviation of the average run length (SDARL) is used as the performance metrics. Our results show that the estimation error results in the significant variation in the ARL distribution. Furthermore, in order to adequately reduce the variability, more phase I samples are required in terms of the SDARL metric than that in terms of the expected ARL metric. In addition, more observations on each sampled profile are suggested to improve the charts' performance, especially for small phase I sample sizes. Finally, an illustrative example is given to show the performance of the proposed zone control charts.     

Extreme statistics from the cosine distribution

The cosine distribution serves as a very good teaching example for which exact moment properties of extreme order statistics can be expressed in terms of elementary functions. This article presents the limiting joint distribution of the extreme order statistics for the cosine distribution. It is shown that burrows'(1986) result is a special case of the result presented in this article.     

Local efficiency of moment estimators in beta-binomial model

In this paper, the beta-binomial model is introduced as a Markov chain. It is shown that the correlated binomial model of Kupper and Haseman (1978) is identical to the additive binomial model of AItham(1978) and both are a first order approximation of the beta-binomial model. For small γ, the local efficiency of the moment estimators for the mean ρ and the extra-binomial variation γ is examined analytically. It is shown that, locally, the moment estimator for p is efficient up to the second order of y. Exact formulae for the relative efficiency are obtained for both the cases with γ known and unknown. Generalization to the unequal sample size case is also carried out. In particular, the gain in efficiency by using the quasi-likelihood estimator instead of the ratio estimator for p is studied when γ is known. These results are in agreement with the Monte Carlo results of Kleinman(1973) and Crowder(1985).     

Combining Univariate Tests for Multivariate Location Problem

In this article, three methods of combining dependent univariate tests are studied. The Bahadur approximate efficiencies are derived under the asymptotic normal assumption. These procedures are applied to the multivariate location problem and compared with two Hotelling-type tests. A Monte Carlo study indicates that in certain cases the powers of the combination methods are much better than Hotelling's T ² and other multivariate nonparametric tests.     

Robust Likelihood Cross-Validation for Kernel Density Estimation

Likelihood cross-validation for kernel density estimation is known to be sensitive to extreme observations and heavy-tailed distributions. We propose a robust likelihood-based cross-validation method to select bandwidths in multivariate density estimations. We derive this bandwidth selector within the framework of robust maximum likelihood estimation. This method establishes a smooth transition from likelihood cross-validation for nonextreme observations to least squares cross-validation for extreme observations, thereby combining the efficiency of likelihood cross-validation and the robustness of least-squares cross-validation. We also suggest a simple rule to select the transition threshold. We demonstrate the finite sample performance and practical usefulness of the proposed method via Monte Carlo simulations and a real data application on Chinese air pollution.     

我国指数基金运作与绩效研究

一、引言指数基金起源于美国 ,1971年美国威弗银行(ＷｅｌｌｓＦａｒｇｏＢａｎｋ)向机构投资者推出了世界上第一只指数基金。指数基金是投资基金的一种类型 ,它是以证券市场的股票指数为投资对象 ,导入指数投资概念 ,采用指数化投资 (也叫资产等级投资或消极投资 )方法 ,跟踪目标指数 ,使自己本身的投资收益率与市场指数收益率基本一致的一种证券投资基金。我国于 1999年 7月 14日正式推出了两只指数基金———基金兴和和基金普丰 ,在设计时均借鉴了国外的运作经验———投资运作跟踪大盘运行 ,同时又体现了自己的独到之处———不完全是纯…     

四川民族地区经济发展与社会稳定战略的实现途径

民族地区的社会稳定与经济发展息息相关。区域资源综合开发和整体开发资源是经济发展和社会稳定的血脉和基础,因此民族地区要要立足特色优势资源,全面落实科学发展观,加强资源整合与综合利用,发展资源节约型和环境友好型产业,构建特色优势产业体系,才能最终促进四川民族地区经济与社会的可持续发展。“十二五”期间,四川民族地区将进入经济发展与社会稳定的重要阶段,本文从加强民族地区整合优势资源,构建优势产业体系出发,阐述了推进传统特色农牧业向现代特色农牧业跨越,以及维护社会稳定的具体措施。