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For linear quantile regression model, this paper proves that the test statistics, besed on smoothed empirical likelihood (SEL) method and least absolute deviation (LAD) method, both converge weakly to a noncentral Chi-square distribution under the local alternatives $H_1:beta=beta_0+a_n$, where $beta$ is the true parameter. Simulation results show that the SEL method is more efficient than the LAD method.     

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This paper is focused on testing the parameters of the quantile regression models. For complete observation, it is shown in literature that the test statistics, based on empirical likelihood (EL) method and smoothed empirical likelihood (SEL) method, both converge weakly to the standard Chi-square distribution $chi_M^2$ under the null hypothesis. For right censored data, the statistics in literature, by the EL method, have a weighted Chi-square limiting distribution, but the weights are unknown. In this paper, we show that the statistics based on the EL method and the SEL method also converge weakly to $chi_M^2$under the null hypothesis, so there is no need to estimate any weights. As its estimating function is smoothed, the SEL method can be Bartlett corrected. Numerical results show that the SEL method, via Bartlett correction, outperforms some recent methods.     

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In this paper, we discuss tail asymptoticsproperties for a class of infinite phase type distributions based onprobability generating function or Laplace-Stieltjes transform. The results show that, unlike finite phase cases, the tail asymptotics for the infinite phase type distributions we considered do not decaygeometrically or exponentially.     

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多元非参数分位数回归常常是难于估计的,为了降低维数同时保持非参数估计的灵活性,人们常常用单指标的方法模拟响应变量的条件分位数.本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础,我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下,得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法,并通过模拟研究说明了本文所提方法变量选择的样本性质.     

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本文对两个样本数据不完全的线性模型展开讨论,其中线性模型协变量的观测值不缺失, 响应变量的观测值随机缺失(MAR).我们采用逆概率加权填补方法对响应变量的缺失值进行补足, 得到两个线性回归模型``完全'样本数据,在``完全'样本数据的基础上构造了响应变量分位数差异的对数经验似然比统计量.与以往研究结果不同的是本文在一定条件下证明了该统计量的极限分布为标准,降低了由于权系数估计带来的误差, 进一步构造出了精度更高的分位数差异的经验似然置信区间.     

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We extend the instrumental variable method for the mean regression models to linear quantile regression models with errors-in-variables. The proposed estimator is consistent and asymptotically normally distributed under some fairly general conditions. Moreover, this approach is practical and easy to implement. Simulation studies show that the finite sample performance of the estimator is satisfactory. The method is applied to a real data study of education and wages.     

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Most regression modeling is based on traditional mean regression which results in non-robust estimation results for non-normal errors. Compared to conventional mean regression, composite quantile regression (CQR) may produce more robust parameters estimation. Based on a composite asymmetric Laplace distribution (CALD), we build a Bayesian hierarchical model for the weighted CQR (WCQR). The Gibbs sampler algorithm of Bayesian WCQR is developed to implement posterior inference. Finally, the proposed method are illustrated by some simulation studies and a real data analysis.     

基于维纳过程步进应力加速退化试验的客观贝叶斯分析

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.     

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Step-stress accelerated degradation test (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable products when the available test items are very few. In this paper, we discuss multiple-steps step-stress accelerated degradation models based on Wiener process, and we apply the objective Bayesian method for such analytically intractable models to obtain the noninformative priors (Jefferys prior and two Reference priors). Moreover, we show that their posterior distributions are proper, and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two Referencepriors. Finally, we present some simulation studies to compare the objective Bayesian estimates with the other Bayesian estimate and the maximum likelihood estimates (MLEs). Simulation results demonstrate the superiority of objective Bayesian analysis method.     

Bayesian Sparse Group Selection

This article proposes a Bayesian approach for the sparse group selection problem in the regression model. In this problem, the variables are partitioned into different groups. It is assumed that only a small number of groups are active for explaining the response variable, and it is further assumed that within each active group only a small number of variables are active. We adopt a Bayesian hierarchical formulation, where each candidate group is associated with a binary variable indicating whether the group is active or not. Within each group, each candidate variable is also associated with a binary indicator, too. Thus, the sparse group selection problem can be solved by sampling from the posterior distribution of the two layers of indicator variables. We adopt a group-wise Gibbs sampler for posterior sampling. We demonstrate the proposed method by simulation studies as well as real examples. The simulation results show that the proposed method performs better than the sparse group Lasso in terms of selecting the active groups as well as identifying the active variables within the selected groups. Supplementary materials for this article are available online.     

基于大样本电梯抽查数据的风险评估Logistic模型

为了提高在用电梯监督抽查工作效率及有效性,在统计分析G市电梯安全监管抽查的大样本数据基础上,构建以电梯使用情况、电梯基本参数及制造维保相关情况等为指标的管理体系。根据电梯抽查数据的实质,先对数据进行变量筛选,然后构建风险分级,最后对前人的方法作出改进形成风险矩阵法并提出以Logistic方法为电梯整机风险建立量化模型,最终形成电梯整机风险评估体系。从理论的角度看,通过使用LIFT统计量和K-S统计量比较两种风险值计算模型,得出用Logistic方法进行风险分层更为准确。而实际的工程应用表明,利用Logistic回归法与基于平均风险值赋权比例法的组合为电梯安全监管抽样调查提供的筛选比例,比现有的方法更合理准确。     

动态异方差随机前沿模型的Bayesian推断

随机前沿模型中如果忽略单边干扰项的异质性(heterogeneity)往往导致错误的效率估计.从个体特征的影响和方差的时变性两方面对单边干扰项进行考虑,提出异方差动态随机前沿模型.利用Gibbs抽样方法对动态异方差随机前沿模型进行Bayesian分析.导出了模型参数的后验条件分布,对中小样本的模拟实验显示在最小后验均方误差准则下得到的参数估计值非常接近真值.对电力公司的实际数据进行分析显示对数无效率项的方差有一定的时变性.     

三参数正态双卵模型Gibbs抽样算法研究

项目反应理论作为一种现代的教育和心理测量方法,凭借其强大的优势和先进性,在实际测量中应用越来越广泛.能否有效地估计模型中的参数是项目反应模型得以应用的前提.本文基于数据扩充技术给出了一种适用于三参数正态双卵模型的Gibbs抽样算法,有效的实现三参数正态双卵模型的贝叶斯分析.最后,通过计算机模拟研究和实例分析对该算法的有效性进行了验证.     

中国地区全要素生产率的Bayesian分析

本文利用全国28个省市自治区的相关数据,以索洛增长方程为基础,采用Bayesian SUR模型以及Gibbs-Importance抽样算法,估算了其资本产出弹性,并在此基础上计算了各地区全要素生产率及其增长率。研究结果表明,科技发展战略对全要素生产率的提高具有显著正效应;随着产业结构调整,资本产出弹性和全要素生产率的关系从正相关逐渐变为负相关,并且由此所表明的地区分工协作特征正逐步显现;内陆地区的地缘经济特征制约了其全要素生产率的进一步提高。