Estimating systems of trending variables

A survey is given of some results on inference in cointegrated systems. We discuss some regression methods, and contrast them with the analysis of the vector autoregressive model. We discuss determination of cointegrating rank and estimation of parameters, as well as asymptotic inference. The problems are treated for 1(1) and for 1(2) variables.     

贝叶斯推理主观性探析——对无差别原则和不变性的考察

作为当代发展最为迅猛的一种科学研究方法——贝叶斯主义方法,尽管已经深入到了科学研究的方方面面,但其先天的“先验”、“主观性”等标签使其陷入了不必要的纷争之中.通过贝叶斯对无差别原则和不变性原理的考察,发现先验概率的无约束即主观性,是贝叶斯主义的一个优点,更重要的是该主观性的产生是由严格的“推理机”——归纳逻辑所定义出的.     

Prequential omnibus goodness-of-fit tests for stochastic processes: A numerical study

This article is a contribution to the study of an omnibus goodness-of-fit (Gof) test based on Rosenblatt Probability Integral Transform (RPIT) within Dawid's prequential framework. This Gof test is easy to use since it has a common test statistic (with apparently the same asymptotic distribution) for a wide range of stochastic models. Intensive Monte-Carlo simulations are presented to investigate the behavior of this test for several stochastic models: renewal, autoregressive (AR, ARMA, ARCH, GARCH) and Poisson processes, generalized linear models... These simulations suggest that the RPIT test could be used to test the fit of a wide range of stochastic models but it may be not powerful when compared to Gof tests specifically designed for the tested processes. It is also conjectured that this test is still appropriate for testing the Gof of any discrete-time stochastic process provided that efficient estimators are used.     

纵向部分线性变系数EV模型的估计

纵向数据是随着时间变化对个体进行重复观测而得到的一种相关性数据,广泛出现在诸多科学研究领域。在对个体进行观测时,测量误差不可避免,忽略测量误差往往会导致有偏估计。本文利用二次推断函数方法研究关于纵向数据的参数部分和非参数部分协变量均含有测量误差的部分线性变系数测量误差(errors-in-variables, EV)模型的估计问题。利用B样条逼近模型中的未知系数函数,构造关于回归参数和B样条系数的偏差修正的二次推断函数以处理个体内相关性和测量误差,得到回归参数和变系数的偏差修正的二次推断函数估计,然后证明了估计方法和结果的渐近性质。数值模拟和实例数据分析结果显示本文提出的方法具有一定的实用价值。     

A Bayesian approach to zero-inflated data in extremes

Abstract

The generalized extreme value (GEV) distribution is known as the limiting result for the modeling of maxima blocks of size n, which is used in the modeling of extreme events. However, it is possible for the data to present an excessive number of zeros when dealing with extreme data, making it difficult to analyze and estimate these events by using the usual GEV distribution. The Zero-Inflated Distribution (ZID) is widely known in literature for modeling data with inflated zeros, where the inflator parameter w is inserted. The present work aims to create a new approach to analyze zero-inflated extreme values, that will be applied in data of monthly maximum precipitation, that can occur during months where there was no precipitation, being these computed as zero. An inference was made on the Bayesian paradigm, and the parameter estimation was made by numerical approximations of the posterior distribution using Markov Chain Monte Carlo (MCMC) methods. Time series of some cities in the northeastern region of Brazil were analyzed, some of them with predominance of non-rainy months. The results of these applications showed the need to use this approach to obtain more accurate and with better adjustment measures results when compared to the standard distribution of extreme value analysis.     

基于协变量平衡加权的平均处理效应的稳健有效估计

倾向性得分是估计平均处理效应的重要工具。但在观察性研究中,通常会由于协变量在处理组与对照组分布的不平衡性而导致极端倾向性得分的出现,即存在十分接近于0或1的倾向性得分,这使得因果推断的强可忽略假设接近于违背,进而导致平均处理效应的估计出现较大的偏差与方差。Li等(2018a)提出了协变量平衡加权法,在无混杂性假设下通过实现协变量分布的加权平衡,解决了极端倾向性得分带来的影响。本文在此基础上,提出了基于协变量平衡加权法的稳健且有效的估计方法,并通过引入超级学习算法提升了模型在实证应用中的稳健性;更进一步,将前一方法推广至理论上不依赖于结果回归模型和倾向性得分模型假设的基于协变量平衡加权的稳健有效估计。蒙特卡洛模拟表明,本文提出的两种方法在结果回归模型和倾向性得分模型均存在误设时仍具有极小的偏差和方差。实证部分将两种方法应用于右心导管插入术数据,发现右心导管插入术大约会增加患者6. 3%死亡率。     

论演绎的辩护

与归纳逻辑类似,演绎逻辑也面临着合理性问题。演绎逻辑的辩护问题是逻辑哲学中的重要问题。人们不能用归纳逻辑为演绎做辩护,用演绎逻辑为演绎做辩护也将导致失败。以往的演绎辩护,除了导致循环论证之外,还另有失败原因。在元语言中为对象语言的理论做辩护,这将导致无限的后退,最终也跳不出语言的范围。演绎逻辑是人们发明出来的推理工具,同时也是一种严格按照规则进行的游戏,人们对它无法做出本体论或认识论的辩护。     

Bayesian estimation and prediction of the intensity of the power law process

In analyzing failure data pertaining to a repairable system, perhaps the most widely used parametric model is a nonhomogeneous Poisson process with Weibull intensity, more commonly referred to as the Power Law Process (PLP) model. Investigations relating to inference of parameters of the PLP under a frequentist framework abound in the literature. The focus of this article is to supplement those findings from a Bayesian perspective, which has thus far been explored to a limited extent in this context. Main emphasis is on the inference of the intensity function of the PLP. Both estimation and future prediction are considered under traditional as well as more complex censoring schemes. Modern computational tools such as Markov Chain Monte Carlo are exploited efficiently to facilitate the numerical evaluation process. Results from the Bayesian inference are contrasted with the corresponding findings from a frequentist analysis, both from a qualitative and a quantitative viewpoint. The developed methodology is implemented in analyzing interval-censored failure data of equipments in a fleet of marine vessels.     

中西思维方式的比较-- 对《尚书·洪范》和《工具论·范畴篇》的分析

从推衍形式及其范畴基础这两个方面比较中西两种思维形式,中国思维形式表现为"纯粹关系映射推衍",其推衍形式是"关系映射",其范畴基础是"纯粹关系";西方思维形式表现为"实体关系套接推衍",其推衍形式是"关系套接",其范畴基础是"实体关系"。对此,可以从《尚书·洪范》和《工具论·范畴篇》这两个中西思维的范本中窥见一斑。