初等概率论附随机过程_钟开莱_中文
初等概率论附随机过程_钟开莱_中文内容提本书系根拐施普林格出版社( Springer-Verlag出版的钟开莱著初等慨率论附随机过程》( Elementary Probabilily Theory with Stoch-astic Processes)1975年第二版译出,鳳书是大学教学教科书,可作为我囯高等学校有关挚业的教学参孝书D2.底等擎校教杂考书初等概率论附隋机过程钟开粟著魏宗舒吕乃刚王万中汪振林举于人兵出新华书店北意发行所发行潜江县印刷厂印装开本?87X10921/32的张12.25字数293,01979年8月第1版1980筇莒月湖北第1次印刷印数1—12,400书号13012·0382定价0.89元第一版序言在过去半个世纪中,概率论从一个较小的孤立的课题发展成为一个与数学许多其它分支相互影响内容宽广而深入的学科,同时,它对各种应用科学,诸如统计学、运筹学、生物学、经济学和心理学的数学化赶着中心作用—这里仅举几个在它们的名种前早已牢固地安上“数理这个前缀词的科学.就率成年的标志反映在该学科教科书内容的改变上,在过去的日子里,这类书的大多数明显分成两种不同的类型,一种是组合的随机游戏,另一种是以正态分布为中心的“误差论”在费勒的经典著作〔见[ Feller11④)于1950年问世后,这一时期就告终止,我第一次讲授的有点份量的穊率论教程就是取材于这部书的原稿.随着时间的推移,概率论及其应用在大学课程中赢得了一个位置,成为许多领域中必修的一门数学学科,现在:这一理论的要点在不同的水上讲授,有时甚至在微积分之前讲授.这本教科书是作为大学二年级水平的门课程而写的,它并不要求对这一学科有任何事先了解,并且头上三章射大部分无需微积分的帮助就可以阅读.接下来的三章则要求懂得如何使用无穷级数及其有关课题的识而对于涉及具有密度的随机变量的讨论,当然要求有某些微积分知识.那些讲解“连续情况”的部分,是很容易与“离散情况”的部分分开的并且可以留到以后去读.头上六章的内容应该成为任何有意义的概率论初级导论的主要部分,在这以后,一个合理的选择包括:7.1普哇松分布,它可插在本课程较前的部分},对3,74,7.6(正方括号内的名字清查阅书术的一般参考文献威席·费勸 Willam Fell〔1906~1970)a11((/868态分布和大数定律)作某种不太深入的阅读,和§8.1(简单随机动,这既有启发性又很有用),所有这些,在二分制学校(→学年分灯两个学期)可以一学期内完成,但对四分制学校(一学年分为四个学期〕要一学期完成的话,就必须作一些削减.明确地说,对这样个短课,第一和第三章可以粗读一下并把打星号的材料路去.无论哪种情况;例如在一个二分之一学年的课程或两个四分之一学年的课程中,只要时间允许,就务必对第七章的正态近似定理作扎实的讲解.最后的第八章,给出马尔可夫链一个完整而初等的描述并且是课程主要郣分在较成熟的水平上的一个推广正态近似定理,连同打星号的§5.3,5.4(序贯抽样和卜耶坛子模型),以及§7.2(普哇松过程),或者再包括附录中的某些补充,这些材料提供了由浅入深、稳步地进人随机过程领城的途径,把这些课题包括在内,本书适合于一→门两个四分之一学年的课程,这也就是我多次对数学科学和学工程的學生讲授的内容,但是,经过头上六章的训练后,读者可以进入如上面提到的费勒专著中一些更深的专题,如果读者具有足够的数学基础,他也有资格选读门严谨的课程,其内容有如我那本较深书 Chung1]中所提供的为了适合课堂之用,如何选择、组织和讲解材料,我确是动了些脑筋,但我却没有试图提供一个装璜精美、适合精确的时间表或程序表的内容,就象大众对快速服务框台要求提供的商品那样因为教师对他的班级恰好需要什么,能作出最好的决定,所以应留給他一定程度的伸缩性和选择性,为了说明主旨和解释清楚,每章开头总包含一些容易阅读的部分,因此教师可以集中注意课文中较严格的方面。每章还包含一些略具挑戕性的课题(例如§.425)以供选择,它们并不是为了刁难初学者,而是想引导他们作进一步的研究,本书始终着重于初等概率论中基本概念和方法透◆2彻和细致的讨论,而修饰或复杂的技巧极少,由于预见到初学者的困难,特地选择许多例题以引起更好的思考这常常是用提和回答一些诱导性的问题来实现的.加入一些历史的、哲学的和个人的注释,可以给这一生动学科增添一总趣味,我希望读者不但从这本书中学到一些东西,还在阅读过程中享受到一定的乐趣头上六章有二百多个习题,最后两章有八十多个习题.许多是容易的,较难的都打上星号,书末附有全部答案.带星号的背和段处理较专门或较细致的内容,可以跳过它们但浏览一下还是值得的任何初等教科书的作者总得感谢无数前人.我个人特别应该致谢的如下: Michel nadzela写出了我1970年在斯坦福大学的饼课笔记, Gian-Carlo Rota见了这份笔记后,推动我把它改写为一本书.DG. Kendall对某几初稿提了意见并进一步给予道义上的支持,JL,Dob自愿阅读大部分手稿并提供许多有益的建议.K.B. Erickson在他所教的课程中用了一部分材料,AA. Halkema审阅了最后一稿并作了许多改进, Dan Rudolph和我一赶看了校样, Perfecto Mary画了讨人喜欢的所有插图Gail Lemmoud用她一贯的高效率和可信任的态度担负打字工作.最后,我非常高兴地感谢我的老出版商 Springer- Verlag米纳我的新书,以开始一套新的大学教程丛书钟开莱1974年3月第二版序言为『改正第一版中的镨误,做了坚决的努力.帮助我完成这工作的有以下各位: Chao Hung-po,J.L.Doob,R.M. Exner,W. H Fleming, A M. Gleason, Karen Kafador, s.H. Polit FhP. van moerbeke. Kafador女士和Poit博土提出了一份特别仔细的建议清单.最使人生气的错误,出现在习题的解答中.我检查了第一至第五章,Chao先生检套了第六至第八章的所这些错误.我强烈地希鲲继线残留在这一范围的镨误不大可能有了.还作了一些小的改进和增加,但在这一点上并不是所有的劝告都可以遵行的.恳切希望使用这本书的人提出批评和意见,以便将来再版中研究采用.我还要感谢 Springer-Verlag的工作人员,他们使这乍书出版后这样快就出了修订版钟开莱目录序■■■↓■■■督■ψ山晉血·■■中■■■血■■■昏4山■■■h■■凸唱昏卿甲噜中自自h唱■■自■第一章集合■自ψ自■■鲁自↓自自鲁■q■_Pψ自卓自卩自自■●■·p■P自卓·■P甲音■号P甲■自白白·音口··血§1.1.祥木集合山中4白■■号司平p■P甲P鲁4p省甲甲■p■甲Pm甲p中甲d◆k中■m§1.2.集合运算§.3.各种关系"甲··d甲m旷音中学中d司甲甲面qmhψb甲ψd面■■日音h暑■"「·■81.4.桁示子h晶甲曾T日甲q甲"甲-甲如■■·P■俨md山h·t血↓包■【■冒习题h日甲日h血■·■幽■b■白■日■■甲■■平曾■「省·甲-l8第二章概率………………………………2§2.1.概率的例了20§2.2.定义和例子了…24§2.3.公理的推论……………………………………………………32豸2.4.独立事供甲噌普P血即白幽备§2.5.算木密度…………………………*44题…5第三计数*…““4933.1.基本法则…493.2,各种取祥方式…………………………………………·5333.分配模型,二项系数…■■■1■甲【■口甲■甲!蚤■■59F3.4,怎样求解………68习题了8第四章随机变量……………………………"“82§4.1.什么是一个随机变量?……■口鲁■甲■■■■82842.随机变量是怎样产生的?……………………"864,3.分布和望………………93§4.4,取整数值的随机变量白■dd4■昏44……………100ε4,5,具存密度的随机变量………4.6.一般情况………参甲"117■鲁■■■b鲁■■■■昏■■■面■鲁4山■【■■■■■…MM…4M]22附录1波雷尔城和一般的随机变虽…■會甲■噜■■鲁?■鲁■血鲁個由[幽噜血_鲁個會■■26第五章条件性和独立性…………………………………………129条件性的例子……………………………………………129§5.2,基木公式血甲嚯噜中■■會會■■血·13585.3.*序贯抽样∵§5.4.*卜里耶的坛子模型………………………………-………15且§5.5.独立性和关联性…………Tψ口山■d聊ψψ司聊■b■■聊血■hbd■4■■面■;聊p159§5.6.*遗传模型……………………………………………171习題………………177第六章平均值,方差和变换…18386.3,期塑的基本性质………………………………r-………………183§6.2,密度的情况『■『■中↓冒4唯中1咽早tT昏中-188§63.乘法定理方差和协方差………193§6.4,多項分布………*…………“…………………………"201落6.5,母函数和其他…………………*…208习题217第七章普咤松分布和正态分布■··『·■·白·ψ司●自■t■·山山2247.1,普哇松分布的模型r…"*…2487z.普哇松过程…………………………………………………23373,由二项分布到正态分布早卜卜吾早4b■444·■!4■■·■已587,4,正态分布會■…………………25375.中心极限定理會■中口血一………-………257§7.6.大数定律…"……"…………264习题………………"…………………272爾录2斯梯林公式和德莫哇佛→拉普拉斯定理276第八章从随机游动到马尔可夫链·279§8、1、流浪者或赌徒朐问题……………………………*……27998,2,板限模型……………………………………………………………286§8.3,转移概率■q『d■跏■卜县啬■警白■■卜■■b冒甲■bP4d■普■中■冒即即……293§8.4,马尔可夫链的基本结构……………………………303§8.5.进一步的发展■凸■Pψ‘■■自■■曾血■血■鲁P■■■日■啁·■4自■日自即■血4自L■血§8.6.意定状态…§8.7,绡束还继续搞下去?4·336习题……………………………*………………………………347附录3鞅甲■dqL■■■■■血■▲dP甲hψ自甲甲■看………36一般参考文献"…."!358只题答案……………359索引…376
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Robust Statistics - 2nd Edition
鲁棒统计，现代统计方法， Robust Statistics第二版，学习现代统计方法R○ BUST STAT|STCSSecond editionPeter j, huberProfessor of Statistics, retiredKlosters SwitzerlandEⅣ ezio m. RonchettiProfessor of StatisticsUniversity of Geneva, SwitzerlandWILEYA JOHn WileY SONS INC. PUBliCAtIONCopyrightc 2009 by John Wiley Sons, Inc. All rights reservedPublished by John Wiley sons, Inc, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the priorwritten permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax978)750-4470,oronthewebatwww.copyrigom. requests to the publisher for permission shouldbe addressed to the permissions department John Wiley sons, Inc., 11 1 River Street, Hoboken, NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp:/www.wileycom/go/permissionLimit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies contained herein may not be suitablefor your situation. You should consult with a professional where appropriate. Neither the publisher norauthor shall be liable for any loss of profit or any other commercial damages, including but not limitedto special, incidental, consequential, or other damagesFor general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For information about wiley products, visit our web site atwww.wileycomLibrary of Congress Cataloging-in-Publication Data:Huber Peter JRobust statistics, second edition/ Peter J. Huber, Elvezio ronchettip. cnIncludes bibliographical references and indeISBN978-0-470-12990-6( cloth)1. Robust statistics. I. Ronchetti. elvezio. II. TitleQA276.H7852009519.5-dc222008033283Printed in the United States of america10987654321To the memory o1John w. tukeyThis Page Intentionally Left BlankCONTENTSPrefacePreface to first editionGeneralities1 Why robust Procedures1. 2 What Should a robust procedure achieve?1.2.1 Robust. Nonparametric and Distribution-Free1.2.2 Adaptive procedures1.2.3 Resistant Procedures1.2. 4 Robustness versus Diagnostics1.2.5 Breakdown point1.3 Qualitative Robustness567888911. 4 Quantitative Robustness1.5 Infinitesimal Aspects141.6 Optimal Robustness171.7 Performance Comparisons18CONTENTS1.8 Computation of robust estimates181.9 Limitations to Robustness Theory202 The Weak Topology and its Metrization23eneral remarks232.2 The Weak Topology232.3 Levy and prohorov metrics272.4 The bounded Lipschitz metric322.5 Frechet and Gateaux derivatives366 Hampels Theorem413 The Basic Types of Estimates453. 1 General Remarks453.2 Maximum Likelihood Type Estimates(M-Estimates)3.2.1 Influence Function of m-estimates73.2.2 Asymptotic Properties of M-Estimates483.2.3 Quantitative and Qualitative Robustness of MEstimates3.3 Linear Combinations of Order Statistics(L-Estimates)3.3.1 Influence Function of -Estimates3.3.2 Quantitative and Qualitative robustness of l-Estimates 593. 4 Estimates Derived from Rank Tests(R-estimates3.4.1 Influence Function of R-Estimates623.4.2 Quantitative and Qualitative robustness of R-Estimates 643.5 Asymptotically Efficient M-, L,and R-Estimates674 Asymptotic Minimax Theory for Estimating Location4.1 General remarks4.2 Minimax bias4.3 Minimax Variance: Preliminaries744. 4 Distributions minimizing fisher Information764.5 Determination of Fo by Variational Methods814.6 Asymptotically Minimax M-Estimates914.7 On the minimax Property for L-and R-estimates954.8 Redescending m-estimates74.9 Questions of Asymmetric Contamination101CONTENTSScale Estimates1055.1 General remarks1055.2 M-Estimates of scale1075.3 L-Estimates of scale5.4 R-Estimates of Scale1125.5 Asymptotically efficient Scale estimates1145.6 Distributions Minimizing fisher Information for Scale5.7 Minimax Properties116 Multiparameter Problemsin Particular Joint Estimationof Location and scale1256. 1 General remarks1256.2 Consistency of M-Estimates1266.3 Asymptotic Normality of M-Estimates1306. 4 Simultaneous m-Estimates of Location and scale1336.5 M-Estimates with Preliminary Estimates of Scale1376.6 Quantitative robustness of Joint Estimates of Location and Scale 1396.7 The Computation of M-Estimates of Scale14368Studentizing1457 Regression1497. 1 General remarks1497. 2 The Classical Linear Least Squares Case1547. 2.1 Residuals and Outliers1587.3 Robustizing the Least Squares Approach1607.4 Asymptotics of robust regression Estimates163741 The Cases hp2→0 and hp→07.5 Conjectures and Empirical Results1687.5.1 Symmetric Error Distributions1687.5.2 The Question of Bias1687.6 Asymptotic Covariances and Their estimation1707. 7 Concomitant Scale estimates1727.8 Computation of Regression M-Estimates1757.8.1 The Scale Step1767.8.2 The Location Step with Modified residuals1787.8.3 The Location Step with Modified Weights179CONTENTS7.9 The Fixed Carrier Case: What Size hi?1867. 10 Analysis of Variance1907. 11 LI-estimates and Median polish1937. 12 Other Approaches to Robust Regression1958 Robust Covariance and Correlation Matrices1998. 1 General remarks8.2 Estimation of Matrix Elements Through robust Variances2038.3 Estimation of Matrix Elements Through robust Correlation2048.4 An Affinely equivariant approach2108.5 Estimates Determined by Implicit Equations2128.6 Existence and Uniqueness of Solutions2148.6. 1 The Scatter estimate v2148.6.2 The Location estimate t2198.6.3 Joint Estimation of t and y2208.7 Influence Functions and Qualitative robustness2208.8 Consistency and asymptotic normality2238.9 Breakdown Point48.10 Least informative distributions2258.1058. 10.2 Covariance2278.11 Some Notes on Computation2339 Robustness of Design2399.1 General remarks2399.2 Minimax Global Fit9.3 Minimax Slope24610 Exact Finite Sample Results24910.1 General Remarks24910.2 Lower and Upper Probabilities and Capacities25010.2.1 2-Monotone and 2-Alternating Capacities25510.2.2 Monotone and Alternating Capacities of Infinite Order 25810.3 Robust Tests25910.3. 1 Particular Cases26510.4 Sequential Tests267
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