Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods

Tanaka (1988) lias derived the influence functions, which are equivalent to the perturbation expansions up to linear terms, of two functions of eigenvalues and eigenvectors of a real symmetric matrix, and applied them to principal component analysis. The present paper deals with the perturbation expansions up to quadratic terms of the same functions and discusses their application to sensitivity analysis in multivariate methods, in particular, principal component analysis and principal factor analysis. Numerical examples are given to show how the approximation improves with the quadratic terms.     

The weighted jackknife for ratio estimation

Using the idea of impirical influence function, Hinkley (1977), the weighted jackknife technique is extended to ratio estimation. A weighted jackknife variance estimator for the ratio estimator is developed. Using the prediction theory approach, the properties of the weighted jackknifed variance estimator are examined. The implications of the failures of regression model on the behaviour of the weighted jackknifed variance estimator, for ratio estimation, are also studied.     

Influence in covariance structure analysis: with an application to confirmatory factor analysis

Influence functions are derived for the parameters in covariance structure analysis, where the parameters are estimated by minimizing a discrepancy function between the assumed covariance matrix and the sample covariance matrix. The case of confirmatory factor analysis is studied precisely with a numerical example. Comparing with a general procedure called one-step estimation, the proposed procedure has two advantages:1) computing cost is cheaper, 2) the property that arbitrary influence can be decomposed into a fi-nite number of components discussed by Tanaka and Castano-Tostado(1990) can be used for efficient computing and the characterization of a covariance structure model from the sensitivity perspective. A numerical comparison is made among the confirmatory factor analysis and some procedures of ex-ploratory factor analysis by using the decomposition mentioned above.     

A class of high-breakdown scale estimators based on subranges

We consider a new class of scale estimators with 50% breakdown point. The estimators are defined as order statistics of certain subranges. They all have a finite-sample breakdown point of [n/2]/n, which is the best possible value. (Here, [...] denotes the integer part.) One estimator in this class has the same influence function as the median absolute deviation and the least median of squares (LMS) scale estimator (i.e., the length of the shortest half), but its finite-sample efficiency is higher. If we consider the standard deviation of a subsample instead of its range, we obtain a different class of 50% breakdown estimators. This class contains the least trimmed squares (LTS) scale estimator. Simulation shows that the LTS scale estimator is nearly unbiased, so it does not need a small-sample correction factor. Surprisingly, the efficiency of the LTS scale estimator is less than that of the LMS scale estimator.     

时代需求对赵树理文风形成的影响——赵树理文风形成原因探析之三

时代需求为赵树理文学主张和实践提供了广阔的天地、肥沃的土壤。抗日战争大环境、积极投身抗战宣传和毛主席《在延安文艺座谈会上的讲话》的发表对赵树理文学创作的重要影响 ,说明了时代需求是赵树理文风形成的主要因素之一。     

论楚辞对汉赋的影响

汉赋“受命于诗人 ,拓宇于《楚辞》。”汉大赋铺张扬厉、结构宏大、语言华丽、句式工整 ,这种审美情趣和特点直接受楚辞的影响 ,故有“楚艳汉侈”之说 ;抒情赋以《楚辞》为模仿对象 ,具有抒情述志 ,注重音韵节奏而篇幅不长等特点 ,它直接脱胎于《离骚》、《九章》。一方面是因为统治者需要歌功颂德 ,文人以辞赋创作作为进仕的手段 ;另一方面文人生活的困顿与挫折 ,诸多悲剧性的人生遭际 ,需要以辞赋写志抒情 ,楚辞也始终在赋家创作中起影响作用。以司马相如《天子游猎赋》为代表的以描写皇宫帝苑和帝王巡狩游宴为主要内容的汉大赋得楚辞之形 ,以贾谊《吊屈原赋》为代表的以抒写个人情志为主的抒情赋得楚辞之神 ,二者对楚辞各取所需而面目各异     

基于投入—产出模型的四川省出口商品结构调整研究

针对出口商品的结构问题,采用投入—产出模型分析了四川省 2007 年投入产出表对该省出口结构合理度,得到了四川省出口商品结构不合理的判断,提出了发展支柱产业、调整经营战略、创立国际品牌等建议。研究结果为四川省调整出口商品结构提供指导。     

论蒋介石的江湖义气观

江湖义气观念浓厚是蒋介石区别于同代其他政治家的一个重要特征。它既反映出蒋介石封建主义的传统价值观 ,又体现了蒋介石作为现代政治家的实用主义色彩。这一切完全是由于近现代中国的特定历史环境所决定的 ,它无论对蒋介石个人还是对国民党及其政府 ,都产生了极为深刻的影响     

论《邯郸记》

汤显祖的《邯郸记》加强了世俗内容和文人自身命运的体验，以及地域色彩的渲染，因而成为一部跨越时空依然余香缭绕的珍品。     

拜登政府对华政策走向及其地缘政治影响:以美国印太战略为视角

拜登政府赞同特朗普政府对华认识,并继承了其对华遏制战略的基本思想,同时加紧实施针对中国的“联盟战略”,拉拢更多盟友,利用国际规则和法律,继续在知识产权、技术转移、补贴、产业政策、科技等领域持续打压中国,严重影响了中国快速发展的进程,增添了中国和平解决台海问题的复杂性与难度。中国必须早作应对。