Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.     

伦理经济原理与市场经济伦理

伦理学和经济学仿佛是互有敌意的兄弟。说它们是兄弟,因为它们都是关于人的行动和决策的理论,都关心行动和决策的合理性和正确性。说它们互有敌意,因为它们的规范性内容似乎是互相矛盾的,伦理学追求至善,而经济学追求效率,至善的东西未必有效率,有效率的东西未必至善;追求至善的好心人未必总是得到好报,追求效率的坏人未必总是得到恶报。怎样解决两者之间的这种矛盾,伦理经济提出了若干基本原理,其中最重要的有:善的三重性(道德、效果和效率)原理;伦理经济的双重性(经济和伦理性质)原理;作为伦理学经济的伦理经济原理(如道德利益相容性原理、普遍利益权重原理等);作为市场经济的伦理预设的伦理经济原理(如契约第三方原理、双重效应原理、超动机原理等)。     

全球视野中的西方历史思想:十个命题

所谓“西方”,本身是一个历史的建构。欧洲特定的文化背景,历史上一系列的文化及社会运动,对历史思想和历史书写都产生了重大影响,使得西方史学具有了一定程度上的独特性,譬如强调进步和发展等等。然而这种独特性并不是一连串独一无二的特征,也不意味着西方历史著作的方式在所有方面都优于其他方式。归根到底,正是不同体系之间的冲突,尤其是不同“力量”之间的动态平衡,才构成西方历史思想和历史书写的特点。     

论停滞与失败--思想意识形态与历史:两个初步的问题(之一)

理学作为一种思想体系受到朝廷的推崇,并作为科举考试的组成部分。在20世纪,对理学的看法发生了分歧。有人认为理学是智识与科学进步的障碍,中国要想走向现代化就必须摆脱理学。关于中国在12世纪后进入长时期停滞的看法,历史学界一般都不赞成了,但读者的这种看法还比较强烈。对于中国历史的一些基本特征的认识需要重新检验,比如中国文化不是只有一个起源;中国并非与外界隔离并拒绝外界影响;中国的政治体制不是绝对独裁;中国文化并没有一个纯正的“正统”或“道统”(orthodox);中国人并非没有自主的完整实体的“自我”观念。学者在实际研究中往往把中国当作一个实体民族或一个连续不断的文明体,这种观念并不太准确,实际是误解了China的原意。     

Investigating impacts of complex sampling on latent growth curve modelling

We investigate the impacts of complex sampling on point and standard error estimates in latent growth curve modelling of survey data. Methodological issues are illustrated with empirical evidence from the analysis of longitudinal data on life satisfaction trajectories using data from the British Household Panel Survey, a national representative survey in Great Britain. A multi-process second-order latent growth curve model with conditional linear growth is used to study variation in the two perceived life satisfaction latent factors considered. The benefits of accounting for the complex survey design are considered, including obtaining unbiased both point and standard error estimates, and therefore correctly specified confidence intervals and statistical tests. We conclude that, even for the rather elaborated longitudinal data models that were considered, estimation procedures are affected by variance-inflating impacts of complex sampling.