Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

权力观念的历史变迁

人类文明由传统社会发展到现代社会的过程中,人们对政治权力的认知与态度实现了以下四种转化;（1）从统治型权力观到服务型权力观;（2）从单向性权力观到双向性权力观;（3）从全能权力观到有限权力观;（4）从强制性权力观到说服性权力观。     

西方近代政治思想对陕西的影响

鸦片战争以后,西方近代政治思想逐渐传入中国,并对地处中国西北内陆、有深厚传统文化底蕴的陕西产生了巨大的冲击。随着西方近代政治学说在陕西传播的深入,西方近代政治思想对陕西近代社会历史发展的影响也愈以明显。     

Testing for No Effect by Cosine Series Methods

The properties of three lack-of-fit tests that are related to non-parametric cosine regression analysis are examined in the context of testing for a constant mean function. Analytic power comparisons of these tests vs a most powerful test are made using intermediate asymptotic relative efficiency. In particular, a data-driven test is produced which is asymptotically as efficient as the most powerful test over a class of alternatives. A small scale simulation experiment is conducted to ascertain the extent that the large sample comparisons are applicable to finite samples.     

Bootstrap tests: how many bootstraps?

In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and propose a simple pretest procedure for choosing the number of bootstrap samples so as to minimize experimental randomness. Simulation experiments suggest that this procedure will work very well in practice.     

司法与行政:中国司法行政化及其检讨

司法行政化是中国司法改革的重大阻碍和重要对象 ,它也是研究司法改革“中端”层面的很好切入。本文从中国司法行政化的宏观观察、症结分析和克服对策三个方面全面阐述了一条新的司法改革路径     

Transformation using ( x + 0.5) to stabilize the variance of populations

Transformation is required to achieve homo-scedasticity when we perform ANOVA to test the effect of factors on population abundance. The effectiveness of transformations decreases when the data contain zeros. Especially, the logarithmic transformation or the Box–Cox transformation is not applicable in such a case. For the logarithmic transformation, 1 is traditionally added to avoid such problems. However, there is no concrete foundation as to why 1 is added rather than other constants, such as 0.5 or 2, although the result of ANOVA is much influenced by the added constant. In this paper, I suggest that 0.5 is preferable to 1 as an added constant, because a discrete distribution defined in {0, 1, 2, . . .} is approximately described by a corresponding continuous distribution defined in (0, ≧) if we add 0.5. Numerical investigation confirms this prediction. Received: October 16, 1998 / Accepted: June 10, 1999     

希腊神话的人文精神

希腊神话是美妙的,它的美是纯粹的、乐观的,没有一点儿人生的凄苦、时世的险恶或惩恶扬善、拯救人类的说教,显示出浪漫的古希腊人“审美重于道德”的价值取向;希腊神话是原欲人性的礼赞,它歌颂性爱、赞美肉体,体现了古希腊人“人性、人权高于一切”的哲学观念和“真即美”的审美标准;希腊神话是乐观主义的源泉,体现出他们为人处世的快乐原则,也表明着古希腊“没有罪恶感”的社会初始阶段特征;希腊神话是力量的颂歌,体现出一种强烈的抗争意识、尚武精神和个人荣誉感,从而演化出西方后世强烈的个体意识……神话的形式会消亡,但它的精神会转化为文化形态而得以存在,得以流传。     

国家与民族地区乡村社会的重组——裕固族大草滩村的个案研究

本文通过分析2003年云南大学对裕固族大草滩村做的调查资料,运用农村社会学的相关理论,从裕固族大草滩村的现有行政体系入手,探讨文化网络内部的历史、民族因素,及其更细微的象征符号。以此,进一步分析国家政权与乡村社会的互动关系,探索国家政权渗透到乡村社会的方式和途径。     

1945年英国大选工党胜出的原因探析

1945年英国大选,工党出人意料地以绝对优势击败长期执政的保守党,成为英国社会的执政党。探析英国工党在1945年大选中胜出的原因,对于我们借鉴外国政党的历史经验,在新时期新形势下加强我们党的执政能力建设、巩固党的执政地位有着重要的作用。