Functional Modelling and Classification of Longitudinal Data*

Abstract. We review and extend some statistical tools that have proved useful for analysing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinite‐dimensional data, and there exists a need for the development of adequate statistical estimation and inference techniques. While this field is in flux, some methods have proven useful. These include warping methods, functional principal component analysis, and conditioning under Gaussian assumptions for the case of sparse data. The latter is a recent development that may provide a bridge between functional and more classical longitudinal data analysis. Besides presenting a brief review of functional principal components and functional regression, we develop some concepts for estimating functional principal component scores in the sparse situation. An extension of the so‐called generalized functional linear model to the case of sparse longitudinal predictors is proposed. This extension includes functional binary regression models for longitudinal data and is illustrated with data on primary biliary cirrhosis.     

变系数变时滞中立型泛函微分方程的振动准则

通过一种直接的方法研究了具有变系数变时滞的超前型一阶中立型泛函方程解的振动性，获得了一系列新的振动准则，改进了许多已知的结果     

论竞争

当代西方社会学最具影响的理论流派功能论和冲突论,它们所看到的社会和谐与社会冲突都是社会的普遍现象,但两种理论各执一端。在整个社会主义初级阶段,既要保持和谐以维护社会结构的相对稳定,又要推进改革以逐步实现社会结构的调整,这就需要在我国的政治、经济和社会生活中普遍引入竞争机制,以促成人们在各个领域中的社会流动。     

Study on the functional liquid of Chinese traditional medicine in anti-anoxic effect

Introduction AkindoffunctionalliquidwasextractedfromcompoundChinesetraditionalmedicinesuchasginseng,danggui,andsoon.Inordertodevelopseriesofhealthfoodsforhuman,wemustfirstobservetheeffectofthe functionalliquidonanti-anoxicinmice.Anti-anoxicofmicewasassayedaccordingtotestmethodsofanti-anoxicfunctionin“Functionalassessmentprocedureandtestmethodsofhealthfood”whichisprovidedby MOH.Tofurtherunderstandthepossiblemechanismsofthefunctionalliquidonanti-anoxicinmice,thestudydiscussedbythewaysofoxyge…     

电磁逆散射问题中的泛函方法

用于电磁逆散射问题中关于未知介质分布的非线性积分方程经离散化后，其相应的矩阵方程通常是病态方程。对于病态的矩阵方程，其解或是不存在或是不唯一。这取决于该矩阵方程是超定的还是欠定的。对于这样的不适定问题，可用一些泛函方法使其转化为适定问题。文中介绍了用于电磁逆散射问题中的最小二乘方法、奇异值分解方法、正则化方法和最大熵方法，并对各种方法的优缺点给出评价。     

掺杂半导体中孤立杂质能级的研究

提出一种计算掺杂半导体中孤立杂质能级的方法,该方法建立在密度函数理论基础之上。在应用时只需考虑杂质原子所在处的电子密度状态,对所研究对象的对称性没有特别的要求。在低掺杂浓度下,理论计算结果与实验结果基本一致。     

自动机泛函ORANPIA—函数程序设计的自动机策略思想

本文明确地提出“将自动机这一概念重新引入到作用式语言中来”。在作用式语言FFP中,为自动机的介入无需设置新的语言成分,而仅仅在FFP语言自身这一级上定义一个新的自动机泛函(名为Oranpia),就可使FFP语言赋有自动机式程序设计风格。此风格有利于我们在不少的实用场合采取“自动机策略思想”来自然地进行有效的程序设计。     

我国金融控股公司的监管问题探讨

分析了金融控股公司给金融监管带来的诸多问题,提出了我国金融监管体制应当朝功能性金融监管方向发展,建立主监管制度以实施对金融控股公司的有效监管,并就监管当局的具体监管措施进行了分析探讨。     

THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

复方中药功能液的抗疲劳功效

根据卫生部《保健食品的功能学评价程序和检验方法》中抗疲劳检验方法进行实验研究,观察复方中药功能液对小白鼠的抗疲劳作用的影响。结果发现:复方中药功能液能明显地延长小白鼠负重游泳时间(P<0.05或P<0.01);明显地增加了运动后小白鼠的肝糖元含量(P<0.01);降低了小白鼠血清中的尿素氮、乳酸脱氢酶、尿激酶等指标,增加了血糖、红细胞、血红蛋白等指标(P<0.05或P<0.01),对白细胞数等指标影响不明显;对小白鼠体重的增长也无显著影响。说明:此人参等复方中药功能液具有明显的抗疲劳作用,还具有推迟小白鼠运动性疲劳的出现和促进疲劳恢复的积极作用。