Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables

We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis–Hastings algorithm.     

基于白化权函数分类区分度的变权灰色聚类

针对灰色聚类指标权重确定的问题,通过定义白化权函数的分类区分度来度量各指标对聚类对象的分类所作的贡献,并据此确定分类指标的权重。在此基础上,提出了变权灰色聚类方法。结果表明,该方法能够融合聚类对象的样本信息和专家的经验,有效确定不同聚类对象的各指标权重,且适用于聚类指标的量纲不同、数量级悬殊较大的情形。最后通过一个实例说明了变权灰色聚类的实用性和有效性。     

Sparse Markov Chains for Sequence Data

Finite memory sources and variable‐length Markov chains have recently gained popularity in data compression and mining, in particular, for applications in bioinformatics and language modelling. Here, we consider denser data compression and prediction with a family of sparse Bayesian predictive models for Markov chains in finite state spaces. Our approach lumps transition probabilities into classes composed of invariant probabilities, such that the resulting models need not have a hierarchical structure as in context tree‐based approaches. This can lead to a substantially higher rate of data compression, and such non‐hierarchical sparse models can be motivated for instance by data dependence structures existing in the bioinformatics context. We describe a Bayesian inference algorithm for learning sparse Markov models through clustering of transition probabilities. Experiments with DNA sequence and protein data show that our approach is competitive in both prediction and classification when compared with several alternative methods on the basis of variable memory length.     

A new model selection procedure based on dynamic quantile regression

In this article, we propose a novel robust data-analytic procedure, dynamic quantile regression (DQR), for model selection. It is robust in the sense that it can simultaneously estimate the coefficients and the distribution of errors over a large collection of error distributions even those that are heavy-tailed and may not even possess variances or means; and DQR is easy to implement in the sense that it does not need to decide in advance which quantile(s) should be gathered. Asymptotic properties of related estimators are derived. Simulations and illustrative real examples are also given.     

Some notes on robust sure independence screening

Sure independence screening (SIS) proposed by Fan and Lv [4 J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc. 96 (2001), pp. 1348–1360. doi: 10.1198/016214501753382273[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] uses marginal correlations to select important variables, and has proven to be an efficient method for ultrahigh-dimensional linear models. This paper provides two robust versions of SIS against outliers. The two methods, respectively, replace the sample correlation in SIS with two robust measures, and screen variables by ranking them. Like SIS, the proposed methods are simple and fast. In addition, they are highly robust against a substantial fraction of outliers in the data. These features make them applicable to large datasets which may contain outliers. Simulation results are presented to show their effectiveness.     

Estimation of Bowley's Coefficient of Skewness in the Presence of Auxiliary Information

In this paper, we suggest regression-type estimators for estimating the Bowley's coefficient of skewness using auxiliary information. To the first degree of approximation, the bias and mean-squared error expressions of the regression-type estimators are obtained, and the regions under which these estimators are more efficient than the conventional estimator are also determined. Further, a general class of estimators of the Bowley's coefficient of skewness is defined along with its properties. A class of estimators based on estimated optimum values is also defined. It is shown to the first degree of approximations that the variance of the class of estimators based on estimated optimum values is the same as that of the minimum variance of the proposed class of estimators. A simulation study is carried out to demonstrate the performance of the proposed difference estimator over the usual estimator.     

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Stratified Random Sampling

This article addresses the problem of estimating the population mean in stratified random sampling using the information of an auxiliary variable. A class of estimators for population mean is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. It has been shown that the proposed class of estimators is better than usual unbiased estimator, usual combined ratio estimator, usual product estimator, usual regression estimator and Koyuncu and Kadilar (2009 Koyuncu, N., Kadilar, C. (2009). Ratio and product estimators in stratified random sampling. J. Statist. Plan. Infere. 139:2552–2558.[Crossref], [Web of Science ®] , [Google Scholar]) class of estimators. The results have been illustrated through an empirical study.     

基于可变强度跳跃-GARCH模型的资产价格跳跃行为分析——以中国上市公司股票市场数据为例

近年来,美国金融危机、欧债危机、地震等突发事件不断冲击着我国金融市场,各类资产价格频繁出现大幅跳动,收益风险短期内急剧扩大。鉴于此,本文构建了门限效应下状态变量依赖自回归强度跳跃-GARCH模型（简称TSD-ARJI-GARCH模型）来探讨股票资产价格随时间平滑波动和大幅度跳跃的双重特征。该模型扩展了现有可变强度跳跃-GARCH模型,克服了片面强调内生或外生因素的局限性,既允许跳跃强度受单个资产异质因素的内生驱动,以刻画跳跃变化的时变性及集聚性,也考虑了外部状态变量影响的门限效应。通过对不同类型中国上市公司股票市场数据的实证分析,验证了该模型对各类上市公司股票资产价格跳跃特征都具有较好的辨别和预测能力,可为动态监管金融资产的跳跃风险提供理论依据。     

制造商供应量变化时同质多物品拍卖价格策略研究

本文分析了制造商供应量变化时、在多个零售商非单位需求情形下的统一价格拍卖与歧视价格拍卖,得到了两种拍卖方式下零售商的报价策略、制造商的价格策略及其相关性质。结果表明:统一价格拍卖中,零售商在低价时所提交数量高于其真实需求,在高价时所提交数量低于其真实需求。歧视价格拍卖中零售商在低价会选择提交自己真实的需求量,在高价会选择提交低于真实的需求量。若参与拍卖的零售商越多,相对歧视价格拍卖,统一价格拍卖提交的需求量扭曲越少,从机制设计的角度来看,制造商更倾向于用统一价格拍卖的方式进行产品批发。