Reliability estimation in multicomponent stress–strength model for Topp-Leone distribution

In this paper, we consider the estimation reliability in multicomponent stress-strength (MSS) model when both the stress and strengths are drawn from Topp-Leone (TL) distribution. The maximum likelihood (ML) and Bayesian methods are used in the estimation procedure. Bayesian estimates are obtained by using Lindley’s approximation and Gibbs sampling methods, since they cannot be obtained in explicit form in the context of TL. The asymptotic confidence intervals are constructed based on the ML estimators. The Bayesian credible intervals are also constructed using Gibbs sampling. The reliability estimates are compared via an extensive Monte-Carlo simulation study. Finally, a real data set is analysed for illustrative purposes.     

异质性数据下广义线性模型的Maximin似然比估计及应用

针对具有多个来源的异质性数据,文献中通常提出复杂程度较高的模型用于描述每个数据子总体的特征,而本文着眼于刻画不同数据子总体的共性进而建立一个简单的模型。在参数估计方面,本文借鉴了普通线性模型的Maximin估计思想,提出了适用于广义线性模型的Maximin似然比估计方法及稀疏结构下的惩罚估计。该方法通过最大化所有子总体中似然比统计量的最小值,构建成一个简单而保守的模型,以减少数据来源较多而呈现的复杂性。所提方法适用于因变量服从正态分布、两点分布、泊松分布等指数族分布的情形,丰富了前人的研究成果,具有更好的实践意义。模拟分析显示,相比于经典的估计方法,Maximin似然比估计方法不仅能够有效地探寻子总体的共性,而且具有较高的样本外预测精度。本文提出的方法也适用于政府统计和经济统计中具有异质性的大型数据集。     

Regression with outlier shrinkage

We propose a robust regression method called regression with outlier shrinkage (ROS) for the traditional n>p$n>p$ cases. It improves over the other robust regression methods such as least trimmed squares (LTS) in the sense that it can achieve maximum breakdown value and full asymptotic efficiency simultaneously. Moreover, its computational complexity is no more than that of LTS. We also propose a sparse estimator, called sparse regression with outlier shrinkage (SROS), for robust variable selection and estimation. It is proven that SROS can not only give consistent selection but also estimate the nonzero coefficients with full asymptotic efficiency under the normal model. In addition, we introduce a concept of nearly regression equivariant estimator for understanding the breakdown properties of sparse estimators, and prove that SROS achieves the maximum breakdown value of nearly regression equivariant estimators. Numerical examples are presented to illustrate our methods.     

Semiparametric latent variable regression models for spatiotemporal modelling of mobile source particles in the greater Boston area

Summary.  Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modelling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies that were conducted at specific household locations as well as 15 ambient monitoring sites in the area. The models allow for both flexible non-linear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalized spline formulation of the model that relates to generalized kriging of the latent traffic pollution variable and leads to a natural Bayesian Markov chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degrees of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately.