Wild Bootstrap of the Sample Mean in the Infinite Variance Case

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986 Wu , C. F. J. ( 1986 ). Jackknife, bootstrap, and other resampling methods . Annals of Statistics 14 : 1261 – 1295 .[Crossref], [Web of Science ®] , [Google Scholar]) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods.     

On Block Skip Free Transition Matrices and First Passage Times

Starting from an abstract setting which extends the property “skip free to the left” for transition matrices to a partition of the state space, we develop bounds for the mean hitting time of a Markov chain to an arbitrary subset from an arbitrary initial law. We apply our theory to the embedded Markov chains associated with the M/G/1 and the GI/M/1 queueing systems. We also illustrate its applicability with an asymptotic analysis of a non-reversible Markovian star queueing network with losses.     

Some characterizations of discrete distributions based on weak records

Let X ₁, X ₂,... be iid random variables (rv's) with the support on nonnegative integers and let (W _n , n≥0) denote the corresponding sequence of weak record values. We obtain new characterization of geometric and some other discrete distributions based on different forms of partial independence of rv's W _n and W _n+r —W _n for some fixed n≥0 and r≥1. We also prove that rv's W ₀ and W _n+1 —W _n have identical distribution if and only if (iff) the underlying distribution is geometric.     

A Characterization of the Normal Family of Distributions Based on the Bias of the Maximum Likelihood Estimator

This paper characterizes the family of Normal distributions within the class of exponential families of distributions, via the structure of the bias of the maximum likelihood estimator Θ _n of the canonical parameter Θ . More specifically, when E _θ ( Θ n ) – Θ = (1/ n ) Q ( Θ ) + o (1/ n ), the equality Q ( Θ ) = 0 proves to be a property of the Normal distribution only. The same conclusion is obtained for the one-dimensional case bt assuming that Q ( Θ ) is a polynomial of Θ .     

ANALYSIS OF DOUBLY CENSORED DATA AND THE HIV INCUBATION PERIOD DISTRIBUTION IN WESTERN AUSTRALIA

The paper analyses the distribution of times from HIV seroconversion to the first AIDS defining illness for a subcohort of the Western Australian HIV Cohort Study for whom the seroconversion date is known to fall within a calendar time window. The analysis is based on a generalised gamma model for the incubation times and a piecewise constant distribution for the conditional times of seroconversion given the seroconversion windows. This allows flexible hazard shapes and also allows comparison of goodness of fit of the gamma and Weibull distributions which are often used for modelling incubation times. Computational issues are discussed. In these data, neither age at seroconversion, nor calendar time of seroconversion, nor the identification of a seroconversion illness appears to afFect incubation distributions. The Weibull distribution appears to provide a reasonable fit. The distribution of times from seroconversion to an HIV-related death is also briefly considered.     

行政中心区位、迁移与城市商圈空间分布——基于动态模糊算法仿真和经验数据的研究

我国城市发展的实践揭示,绝大多数城市的行政中心所在区域不仅是政治中心,也是商业中心;行政中心迁移往往带来迁入地零售商业的爆发式增长,行政中心 区位和迁移与城市商圈空间分布之间有着显著关联.文章通过动态模糊算法仿真分析发现:行政中心对其空间所在区域的商圈发展有积极的正向影响;行政中心空间区位迁移与城市商圈空间结构演化存在显著的空间耦合互动,即迁入区域的商圈发展将显著加速,特别是区域内新商圈成形将明显加速,对迁出区域商圈的影响则相对不明显;城市商圈空间分布发展显著变化.最后,以长沙市的经验数据验证了仿真模型的可靠性.     

样本选择参数分位回归模型及其在工资分布分解中的应用

在工资差距分解问题中,研究者经常会遇到样本选择偏差问题,直接忽略会导致最终估计结果产生严重偏差,同时在众多工资差距分解方法中,相比于均值分解,分布分解方法更受研究者青睐。针对参数分位回归,本文首次提出可加形式与非可加形式的样本选择参数分位回归（SSPQR）模型,并基于这两类样本选择参数分位回归模型给出修正样本选择偏差后的参数分位回归工资差距分布分解方法。运用上述方法及已有的工资分布分解方法,借助CHNS2015年度城镇数据,本文研究了我国城镇男女工资差距及差距分解问题,得出以下结论：①男女工资差距主要来源是性别歧视问题;②经过样本选择偏差修正后,实际的工资差距更大,歧视问题更严重;③男女工资差距程度在不同分位点上结果不同,换句话说,我们不能简单地仅从平均水平来判断工资差距程度;④与其他已有方法计算结果比较发现,SSPQR计算的工资差距程度更大。     

The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008 Diongue, A.K., Guégan, D. (2008). Estimation of k-Factor GIGARCH Process: A Monte Carlo Study. Communications in Statistics-Simulation and Computation 37:2037–2049.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.     

Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics

We propose an influence diagnostic methodology for linear regression models with stochastic restrictions and errors following elliptically contoured distributions. We study how a perturbation may impact on the mixed estimation procedure of parameters in the model. Normal curvatures and slopes for assessing influence under usual schemes are derived, including perturbations of case-weight, response variable, and explanatory variable. Simulations are conducted to evaluate the performance of the proposed methodology. An example with real-world economy data is presented as an illustration.     

Variable selection in elliptical linear mixed model

Variable selection in elliptical Linear Mixed Models (LMMs) with a shrinkage penalty function (SPF) is the main scope of this study. SPFs are applied for parameter estimation and variable selection simultaneously. The smoothly clipped absolute deviation penalty (SCAD) is one of the SPFs and it is adapted into the elliptical LMM in this study. The proposed idea is highly applicable to a variety of models which are set up with different distributions such as normal, student-t, Pearson VII, power exponential and so on. Simulation studies and real data example with one of the elliptical distributions show that if the variable selection is also a concern, it is worthwhile to carry on the variable selection and the parameter estimation simultaneously in the elliptical LMM.