函数型数据回归分析综述

随着计算机储存能力和在线观测技术的提高,当今数据越来越多的以曲线和图像的形式存在.曲线和图像数据两个最显著的特征是高维和相邻数据间高度相关.这些特征使得传统的多元统计分析方法不再适合,而函数型数据在处理曲线和图像数据中具有无可比拟的优势.近年来各种各样的函数型数据分析方法得以发展,其中包括数据的对齐、主成分分析、回归、分类、聚类等.本文主要介绍函数型数据回归分析研究的起源、发展及最新进展.具体地,本文首先介绍函数型数据的概念;其次介绍函数型主成分分析方法;再次着重介绍函数型回归模型的估计、变量选择和检验方法;最后将简要探讨函数型数据未来的可能发展方向.     

关于概率空间与次线性期望空间中的随机变量一致可积性的一个注记（英文）

在这篇注记中我们讨论随机变量的一致可积性.在概率空间中,我们引进了随机变量一致可积性的两个新的定义,并证明了他们与经典定义等价.在次线性期望空间中,我们给出了随机变量一致可积性的德拉瓦利普桑准则,并作了一些其它讨论.     

心形图的匹配能序及Hosoya指标排序

以G(a, 4, b)(a 1, b 1)表示a+b+4个点的心形图.从匹配多项式的定义出发,通过递推关系式刻画出了这类心形图的匹配能级和它们的Hosoya指标的全排序.     

相依删失下基于连接函数的参数模型的统计分析

在临床数据的收集中,由于竞争性风险或者病人的退出可能导致数据删失.删失数据的统计分析大多是基于独立删失的假定进行的.而实际情况中,数据的删失往往是非独立的,即删失变量和失效时间变量是相关的.相依删失使得原本复杂的删失数据处理变得更加困难.在本文中,假定删失变量和失效时间变量的联合分布可以用它们边际分布的连接函数函数表示,在给定连接函数下,得到了比例风险模型的极大似然估计.模拟计算显示,如果删失假定成立,本文所采用方法比独立删失假定下的估计方法更准确.     

基于置信分布的多个对数正态总体的公共均值的置信区间的构建（英文）

在实际应用中需要拟合正的偏态数据时,对数正态分布是通常的选择.当通过多重比较确定了多个对数正态分布总体的均值相同时,如何能够利用更多的信息,同时使用这些对数正态分布总体的信息来构建公共均值的置信区间成为了众多学者颇为关注的问题.本篇文章提出了一种新的基于置信分布的方法来构建多个对数正态总体公共均值的置信区间,该方法通过对相关量的样本方差进行加权来提高效率.进而对文中提出的基于置信分布的置信区间的构建方法进行了蒙特卡洛模拟研究,模拟结果表明,我们提出的构建方法可以得到很好的覆盖概率和较短的区间宽度.文章的最后用三个实际数据来验证了文中所提出方法的表现.     

强混合样本且含附加信息情形M估计和分位数估计的渐近性质（英文）

在强混合样本且含附加信息情形,本文采用经验似然方法提出了一类新的M估计和新的分位数估计.结果表明,本文提出的M估计和分位数估计具有相合性和渐近正态性,且其渐近方差比一般M估计和分位数估计的渐近方差小.     

重复数据空间点过程的非参数强度函数估计的渐进性质（英文）

在重复数据的情况下,我们给出了非齐次点过程强度函数的核估计.并研究了该估计的均方差与积分均方差的渐进性质.对于核估计的窗宽选择,我们给出了两种不同的方法,并用模拟的方法比较了这两种方法的效率.     

基于维纳过程步进应力加速退化试验的客观贝叶斯分析

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.     

Mean values of certain zeta-functions on the critical line

Department of Mathematics, University of Belgrade (Yugoslavia). Department of Mathematics, University of Naples (Italy). Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 29, No. 4, pp. 701–714, October–December, 1989.     

与多值随机微分方程相关马氏半群的无穷小生成元（英文）

当多值随机微分方程的扩散及漂移系数满足利普希兹连续性条件时,我们考虑其解的无穷小生成元问题.为了找出该无穷小生成元的核,我们研究了对应的多值椭圆方程及其粘性解.     

岭回归估计的向量参数方法

本文提出岭回归估计的向量参数方法,选择均方误差函数的负梯度方向作为参数向量方向,根据均方误差与拟合误差的预期约束条件选择确定参数向量模长.文中获得了两个单调性结论,向量参数岭回归估计的均方误差是参数向量模长的单调减函数,而拟合误差是参数向量模长的单调增函数.基于两类误差的单调性结论,本文创建了关于两类误差的预期约束条件,预期条件约束下的向量参数岭回归方法有望成为兼备均方误差次优与拟合误差适度的双赢估计.文章最后是一个应用实例.     

q-Discretization of the two-dimensional Toda equations

q-Discrete versions of the two-dimensional Toda molecule equation and the two-dimensional Toda lattice equation are proposed through the direct method. The Bäcklund transformation and the Lax pair of the former are obtained. Moreover, the reduction to theq-discrete cylindrical Toda equations is also discussed.Department of Electronical Engeneering, Doshisha University, Kyoto 610-03, Japan. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan. (On leave from Department of Applied Mathematics, Faculty of Engineering, Hiroshima University.) Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 390–398, June, 1994.     

Mapping deontic operators to abductive expectations

Deontic concepts and operators have been widely used in several fields where representation of norms is needed, including legal reasoning and normative multi-agent systems. The EU-funded SOCS project has provided a language to specify the agent interaction in open multi-agent systems. The language is equipped with a declarative semantics based on abductive logic programming, and an operational semantics consisting of a (sound and complete) abductive proof procedure. In the SOCS framework, the specification is used directly as a program for the verification procedure. In this paper, we propose a mapping of the usual deontic operators (obligations, prohibition, permission) to language entities, called expectations, available in the SOCS social framework. Although expectations and deontic operators can be quite different from a philosophical viewpoint, we support our mapping by showing a similarity between the abductive semantics for expectations and the Kripke semantics that can be given to deontic operators. The main purpose of this work is to make the computational machinery from the SOCS social framework available for the specification and verification of systems by means of deontic operators. Marco Alberti received his laurea degree in Electronic Engineering in 2001 and his Ph.D. in Information Engineering in 2005 from the University of Ferrara, Italy. His research interests include constraint logic programming and abductive logic programming, applied in particular to the specification and verification of multi-agent systems. He has been involved as a research assistants in national and European research projects. He currently has a post-doc position in the Department of Engineering at the University of Ferrara. Marco Gavanelli is currently assistant professor in the Department of Engineering at the University of Ferrara, Italy. He graduated in Computer Science Engineering in 1998 at the University of Bologna, Italy. He got his Ph.D. in 2002 at Ferrara University. His research interest include Artificial Intelligence, Constraint Logic Programming, Multi-criteria Optimisation, Abductive Logic Programming, Multi-Agent Systems. He is a member of ALP (the Association for Logic Programming) and AI*IA (the Italian Association for Artificial Intelligence). He has organised workshops, and is author of more than 30 publications between journals and conference proceedings. Evelina Lamma received her degree in Electronic Engineering from University of Bologna, Italy, in 1985 and her Ph.D. degree in Computer Science in 1990. Currently she is Full Professor at the Faculty of Engineering of the University of Ferrara where she teaches Artificial Intelligence and Foundations of Computer Science. Her research activity focuses around: – programming languages (logic languages, modular and object-oriented programming); – artificial intelligence; – knowledge representation; – intelligent agents and multi-agent systems; – machine learning. Her research has covered implementation, application and theoretical aspects. She took part to several national and international research projects. She was responsible of the research group at the Dipartimento di Ingegneria of the University of Ferrara in the UE ITS-2001-32530 Project (named SOCS), in the the context of the UE V Framework Programme - Global Computing Action. Paola Mello received her degree in Electronic Engineering from the University of Bologna, Italy, in 1982, and her Ph.D. degree in Computer Science in 1989. Since 1994 she has been Full Professor. She is enrolled, at present, at the Faculty of Engineering of the University of Bologna (Italy), where she teaches Artificial Intelligence. Her research activity focuses on programming languages, with particular reference to logic languages and their extensions, artificial intelligence, knowledge representation, expert systems with particular emphasis on medical applications, and multi-agent systems. Her research has covered implementation, application and theoretical aspects and is presented in several national and international publications. She took part to several national and international research projects in the context of computational logic. Giovanni Sartor is Marie-Curie professor of Legal informatics and Legal Theory at the European University Institute of Florence and professor of Computer and Law at the University of Bologna (on leave), after obtaining a PhD at the European University Institute (Florence), working at the Court of Justice of the European Union (Luxembourg), being a researcher at the Italian National Council of Research (ITTIG, Florence), and holding the chair in Jurisprudence at Queen’s University of Belfast (where he now is honorary professor). He is co-editor of the Artificial Intelligence and Law Journal and has published widely in legal philosophy, computational logic, legislation technique, and computer law. Paolo Torroni is Assistant Professor in computing at the Faculty of Engineering of the University of Bologna, Italy. He obtained a PhD in Computer Science and Electronic Engineering in 2002, with a dissertation on logic-based agent reasoning and interaction. His research interests mainly focus on computational logic and multi-agent systems research, including logic programming, abductive and hypothetical reasoning, agent interaction, dialogue, negotiation, and argumentation. He is in the steering committee of the CLIMA and DALT international workshops and of the Italian logic programming interest group GULP.     

一类非局部Cahn-Hilliard方程弱解的存在唯一性

研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性.     

Smoothly truncated stable distributions,GARCH-models,and option pricing

Although asset return distributions are known to be conditionally leptokurtic, this fact has rarely been addressed in the recent GARCH model literature. For this reason, we introduce the class of smoothly truncated stable distributions (STS distributions) and derive a generalized GARCH option pricing framework based on non-Gaussian innovations. Our empirical results show that (1) the model’s performance in the objective as well as the risk-neutral world is substantially improved by allowing for non-Gaussian innovations and (2) the model’s best option pricing performance is achieved with a new estimation approach where all model parameters are obtained from time-series information whereas the market price of risk and the spot variance are inverted from market prices of options. The paper subsumes a previous one under the title “A New Class of Probability Distributions and Its Application to Finance”. The authors gratefully acknowledge comments made by seminar participants at University of California, Santa Barbara, University of Washington, Seattle, Hochschule für Banken, Frankfurt, Cornell University, Princeton University, American University, Washington DC, and the Risk Management and Financial Engineering Conference held in Gainesville, FL in April 2005. All views and opinions expressed in this article are strictly those of the author and do not necessarily represent the views of Sal. Oppenheim.     

Judson Jerome: The American Academy 1970

Abstract

The Forging of an Aristocracy: Harvard and the Boston Upper Class, 1800–1870, by Ronald Story, Middletown, Connecticut: Wesleyan University Press, 1980, (Distributed by Columbia University Press), 256 pages, $20.00.     

Philip Holgate (1934-1993)

Philip Holgate was born in Chesterfield on 8 December 1934.His family moved from Derbyshire to Devon in 1945, and he waseducated at Newton Abbot Grammar School from 1945 to 1952, andthe University College of the South-West (now Exeter University,but which then awarded London degrees) from 1952 to 1955. Hequalified as both a teacher (King's College, London, 1955–56)and a statistician (University College, London, 1956–57). After teaching mathematics and physics at Burgess Hill School,in Hampstead and then in Borehamwood, Philip joined the StatisticsSection at Rothamsted Experimental Station (1961–62).He then spent five years in the Biometrics Section of the NatureConservancy. His first publications date from this period, andthe interests he acquired then were to develop into what becamehis most enduring, and distinctive, scientific interests. Philip joined the Department of Statistics, Birkbeck College,University of London, in 1967, and remained at Birkbeck forthe rest of his career, until his death from a heart attackon 13 April 1993.     

Book Reviews

The Theory of Unitary Group Representations, by George W. Mackey. Chicago Lectures in Mathematics, University of Chicago Press, 1976. 372 pp. (£4.95).

Automatic Continuity of Linear Operators, by Allan M. Sinclair. Cambridge University Press, 92 pp. (£6.95).     

随机利率下DC型养老金的随机微分博弈

本文研究了Vasicek随机利率下DC型养老金的随机微分博弈.金融市场是博弈的"虚拟"手,博弈中养老金计划投资者占主导.研究目标是:通过养老金计划投资者和金融市场之间的博弈,寻找最优的策略使得终止时刻财富的期望效用达到最大.在幂效用函数下,运用随机控制理论求得了最优策略和值函数的显式解.最后,解释了所研究的结果在经济上的意义,并通过数值计算分析了一些参数对最优策略的影响.     

Higher operations on the Hochschild complex

University of Pennsylvania and Princeton University. University of Pennsylvania. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 1, pp. 1–6, January–March, 1995.