Conditional Functional Principal Components Analysis

Abstract.  This work proposes an extension of the functional principal components analysis (FPCA) or Karhunen–Loève expansion, which can take into account non-parametrically the effects of an additional covariate. Such models can also be interpreted as non-parametric mixed effect models for functional data. We propose estimators based on kernel smoothers and a data-driven selection procedure of the smoothing parameters based on a two-step cross-validation criterion. The conditional FPCA is illustrated with the analysis of a data set consisting of egg laying curves for female fruit flies. Convergence rates are given for estimators of the conditional mean function and the conditional covariance operator when the entire curves are collected. Almost sure convergence is also proven when one observes discretized noisy sample paths only. A simulation study allows us to check the good behaviour of the estimators.     

Genetic algorithms for numerical optimization

Genetic algorithms (GAs) are stochastic adaptive algorithms whose search method is based on simulation of natural genetic inheritance and Darwinian striving for survival. They can be used to find approximate solutions to numerical optimization problems in cases where finding the exact optimum is prohibitively expensive, or where no algorithm is known. However, such applications can encounter problems that sometimes delay, if not prevent, finding the optimal solutions with desired precision. In this paper we describe applications of GAs to numerical optimization, present three novel ways to handle such problems, and give some experimental results.     

论世界儿童立法的趋同化--兼对完善中国儿童立法的几点思考

法律的趋同化是全球化背景下的一个世界性潮流.法律趋同化发展在儿童立法领域呈现出两个明显的历史阶段,即以1899年美国伊利诺斯州<少年法庭法>为标志的第一个历史阶段和以1989年联合国<儿童权利公约>为标志的第二个历史阶段.各国儿童立法的趋同化及其与国际立法的协调也是随着儿童立法趋同化发展而不断发展.中国儿童立法应顺应世界儿童立法趋同化发展的历史潮流,大胆借鉴和吸收国际上成功的实践经验,加快完善中国儿童立法的步伐;加快对现有法律法规的修改完善和新法的制定,完善少年司法制度,发挥非政府组织的作用,培养专业的少年法官和儿童法律工作者.     

Nonparametric M-regression with free knot splines

Many problems of practical interest can be formulated as the nonparametric estimation of a certain function such as a regression function, logistic or other generalized regression function, density function, conditional density function, hazard function, or conditional hazard function. Extended linear modeling provides a convenient theoretical framework for using polynomial splines and their selected tensor products in such function estimation problems and especially for obtaining rates of convergence of the resulting estimates in a unified manner. For a long time the theoretical results were restricted to fixed knot splines and to log-likelihood functions that were twice continuously differentiable. Recently, Stone and Huang extended the theory to handle free knot splines. In the present paper, the theory is further extended to handle contexts in which the log-likelihood function may not be differentiable. Specifically, we establish rates of convergence for estimation based on free knot splines in the context of nonparametric regression corresponding to M-estimates, which includes least absolute deviations (LAD) regression, quantile regression, and robust regression as special cases.     

A copula‐graphic estimator for the conditional survival function under dependent censoring

Rivest Wells (2001) showed that in situations where the dependence between a lifetime and a censoring variable can be modeled by a given Archimedean copula, the copula‐graphic estimator of Zheng Klein (1995) has an explicit form. The authors extend this work to the fixed design regression case. They show that the copula‐graphic estimator then has an asymptotic representation and a Gaussian limit. They also assess the influence of a misspecified copula function on the performance of the estimator. Their developments are illustrated with data on the survival of the Atlantic halibut.     

我国国企集团组织趋同现象研究

纯粹的经济因素———技术环境或竞争形式,都不能作为影响企业组织形态与策略选择的唯一解释。我国国企集团的形成是中央政策主导、股票市场的诱因、地方政府的机会主义以及企业间相互模仿的结果,而这种制度环境压力使组织结构趋同。然而不顾原有社会制度环境的特质,希望借用或移植一个本质不同的外来设计,仓促将国企集团化,尽管外形相似却不能获得预期的收益。     

全球化与文化多元趋同趋势

全球化是世界每个民族、每个国家都无法回避的客观趋势,它给文化界带来的一个重大影响就是引起 了多元文化的冲突与整合,整合的结果应是多元文化趋同趋势,走向多元一体的过程。     

科学主义思潮在当代哲学中的命运

"科学主义"思潮作为西方自然科学发展的必然产物,其历史功绩不可否认.科学主义意识形态化后所造成的话语霸权曾对文化多元性的发展产生巨大的破坏作用,对社会生活产生多方面的影响,这也是"科学主义批判"产生的主要原因.在当代哲学情境下,科学主义思潮并未在强烈的"批判"下慢慢消亡,而是走向了一种更趋合理的发展方向-科学主义与人本主义的协调发展.     

Do bootstrap confidence procedures behave well uniformly in P?

An important statistical problem is to construct a confidence set for some functional T(P) of some unknown probability distribution P. Typically, this involves approximating the sampling distribution J_n(P) of some pivot based on a sample of size n from P. A bootstrap procedure is to estimate J_n(P) by J_n(&Pcirc;_n), where P?_n is the empirical measure based on a sample of size n from P. Typically, one has that J_n(P) and J_n(P?_n) are close in an appropriate sense. Two questions are addressed in this note. Are J_n(P) and J_n(P?_n) uniformly close as P varies as well? If so, do confidence statements about T(P) possess a corresponding uniformity property? In the case T(P) = P, the answer to the first questions is yes; the answer to the second is no. However, bootstrap confidence statements about T(P) can be made uniform over a restricted, though large, class of P. Similar results apply to other functional T(P).     

Penalized likelihood regression: General formulation and efficient approximation

The authors consider a formulation of penalized likelihood regression that is sufficiently general to cover canonical and noncanonical links for exponential families as well as accelerated life models with censored survival data. They present an asymptotic analysis of convergence rates to justify a simple approach to the lower‐dimensional approximation of the estimates. Such an approximation allows for much faster numerical calculation, paving the way to the development of algorithms that scale well with large data sets.