数理统计学导论
2012-6
机械工业出版社
（美）Robert V. Hogg,（美）Joseph W. McKean,（美）Allen T. Craig
694
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这本经典教材保持着一贯的风格，清晰地阐述基本理论，并且为了更好地让读者理解数理统计，还提供了一些重要的背景材料。内容覆盖估计和测试方面的古典统计推断方法，并深入介绍了充分性和测试理论，包括一致最佳检验和似然率。书中含有大量实例和练习，便于读者理解和巩固所学知识。
作者：（美国）霍格（Robert V.Hogg） （美国）Joseoh W.McKean （美国）Allen T.Craig 霍格（Robert V.Hogg），艾奥瓦大学统计与精算科学系教授，自1948年开始任教于艾奥瓦大学，在此从事教学和管理工作50多年，并帮助筹建了统计与精算科学系。他曾担任美国统计协会（ASA）主席，获得过包括美国数学协会杰出教育奖在内的多项教学奖。 Joseph W.McKean，西密歇根大学统计系教授，ASA会士。他在线性、非线性、混合模型的稳健非参数处理方面已发表多篇论文，主要讲授统计学、概率论、统计方法、非参数理论等课程。 Allen T.Craig，艾奥瓦大学教授，已于1970年退休。他曾担任美国数理统计学会（IMS）第一任秘书长，发起并参与了本书的撰写工作。
Preface
1 Probability and Distributio
1．1 Introduction
1．2 Set Theory
1．3 The Probability Set Function
1．4 Conditional Probability and Independence
1．5 Random Variables
1．6 Discrete Random Variables
1．6．1 naformatio
1．7 Continuous Random Variables
1．7．1 naDSformatio
1．8 Expectation of a Random Variable
1．9 Some Special Expectatio
1．10 Important Inequalities
2 Multivariate Distributio
2．1 Distributio of Two Random Variables
2．1．1Expectation
2．2 naformatio：Bivariate Random Variables
2．3 Conditional Distributio and Expectatio
2．4 The Correlation Coefficient
2．5 Independent Random Variables
2．6 Exteion to Several Random Variables
2．6．1*Multivariate Variance-Covariance Matrix
2．7 naformatio for Several Random Variables
2．8 Linear Combinatio of Random Variables
3 Some Special Distributio
3．1 The Binomial and Related Distributio
3．2 The Poisson Distribution
3．3 The Г，χ2，andβ Distributio
3．4 The Normal Distribution
3．4．1Contaminated Normals
3．5 The Multivariate Normal Distribution
3．5．1*Applicatio
3．6 t-and F-Distributio
3．6．1 The t-distribution
3．6．2 The F-distribution
3．6．3 Student’S Theorem
3．7 Mixture Distributio
4 Some Elementary Statistical Inferences
4．1 Sampling and Statistics
4．1．1 Histogram Estimates of pmfs and pdfs
4．2 Confidence Intervals
4．2．1Confidence Intervals for Difference in Mea
4．2．2Confidence Interval for Difference in Proportio
4．3 Confidence Intervals for Paramete of Discrete Distributio
4．4 CIrder Statistics
4．4．1Quantiles
4．4．2Confidence Intervals for Quantiles
4．5 Introduction to Hypothesis Testing
4．6 Additional Comments About Statistical Tests
4．7 Chi-Square Tests
4．8 The Method of Monte Carlo
4．8．1 Accept-Reject Generation Algorithm
4．9 Bootstrap Procedures
4．9．1 Percentile Bootstrap Confidence Intervals
4．9．2Bootstrap Testing Procedures
4．10 *Tolerance Limits for Distributio
5 Coistency and Limiting Distributio
5．1 Convergence in Probability
5．2 Convergence in Distribution
5．2．1Bounded in Probability
5．2．2 △-Method
5．2．3 Moment Generating Function Technique
5．3 Central Limit Theorem
5．4 *Exteio to Multivariate Distributio
6 Maximum Likelihood Methods
6．1 Maximum Likeli．hood Estimation
6．2 Rao-Cram6r Lower Bound and E伍ciency
6．3 Maximum Likelihood Tests
6．4 Multiparameter Case：Estimation
6．5 Multiparameter Case：Testing
6．6 The EM Algorithm
7 Sufficiency
7．1 Measures of Quality of Estimato
7．2 A Su伍cient Statistic for a Parameter
7．3 Properties of a Sufficient Statistic
7．4 Completeness and Uniqueness
7．5 The Exponential Class of Distributio
7．6 Functio of a Parameter
7．7 The Cuse of Several Paramete
7．8 Minimal Sufficiency and Ancillary Statistics
7．9 Sufficiency,Completeness．and Independence
8 Optimal Tests of Hypotheses
8．1 Most Powerful Tests
8．2 Uniformly Most Powerful Tests
8．3 Likelihood Ratio Tests
8．4 The Sequential Probability Ratio Test
8．5Minimax and Classification Procedures
8．5．1 Minimax Procedures
8．5．2 Classification
9 Inferences About Normal MOdels
9．1 Quadratic Forms
9．2 One-Way ANOVA
9．3 Noncentralχ2and F-Distributio
9．4 Multiple Compariso
9．5 The Analysis of Variance
9．6 A Regression Problem
9．7 A Test of Independence
9．8 The Distributio of Certain Quadratic Forms
9．9 The Independence of Certain Quadratic Forills
10 Nonparametric and Robust Statistics
10．1 Location Models
10．2 Sample Median and the Sign Test
10．2．1 Asymptotic Relative Efficiency
10．2．2 Estimating Equatio Based on the Sign Test
10．2．3 Confidence Interval for the Median
10．3 Signed-Rank Wilcoxon
10．3．1 Asymptotic Relative Emciency
10．3．2 Estimating Equatio Based on Signed-Rank Wilcoxon
10．3．3 Confidence Interval for the Median
10．4 Mann-Whitnev-Wilcoxon Procedure
10．4．1 Asymptotic Relative Efficiency
10．4．2 Estimating Equatio Based on the Mann-Whitney-Wilcoxon
10．4．3 Confidence Interval for the Shift Parameter △
10．5 General Rank Scores
10．5．1 Efficacy
10．5．2 Estimating Equatio Based on General Scores
10．5．3 0ptimization：Best Estimates
10．6 Adaptive Procedures
10．7 Simple Linear Model
10．8 Measures of Association
10．8．1 Kendall’S т
10．8．2 Spearman’S Rho
10．9 Robust Concepts
10．9．1 Location Model
10．9．2 Linear Model
11 Bayesian Statistics
11．1 Subjective Probability
11．2 Bayesian Procedures
11．2．1 Prior and Posterior Distributio
11．2．2 Bayesian Point Estimation
11．2．3 Bayesian Interval Estimation
11．2．4 Bayesian Testing Procedures
11．2．5 Bayesian Sequential Procedures
11．3 More Bayesian Terminology and Ideas
11．4 Gibbs Sampler
11．5 Modern Bayesian Methods
11．5．1 Empirical Bayes
A Mathematical Comments
A．1 Regularity Conditio
A．2 Sequences
B R Functio
C Tables of Distributio
D Lists of Common Distributio
E References
F Awe to Selected Exercisds
Index
版权页： 插图： 1.4.27.Each bag in a large box contains 25 tulip bulbs.It is known that 60% of the bags contain bulbs for 5 red and 20 yellow tulips,while the remaining 40% of the bags contain bulbs for 15 red and 10 yellow tulips.A bag is selected at random and a bulb taken at random from this bag is planted. (a)What is the probability that it will be a yellow tulip? (b)Given that it is yellow,what is the conditional probability it comes from a bag that contained 5 red and 20 yellow bulbs? 1.4.28.A bowl contains 10 chips numbered 1,2,…,10,respectively.Five chips are drawn at random,one at a time,and without replacement.What is the probability that two even-numbered chips are drawn and they occur on even-numbered draws? 1.4.29.A person bets 1 dollar to b dollars that he can draw two cards from an ordinary deck of cards without replacement and that they will be of the same suit.Find b so that the bet is fair.1.4.30(Monte Hall Problem).Suppose there are three curtains.Behind one curtain there is a nice prize,while behind the other two there are worthless prizes.A contestant selects one curtain at random,and then Monte Hall opens one of the other two curtains to reveal a worthless prize.Hall then expresses the willingness to trade the curtain that the contestant has chosen for the other curtain that has not been opened.Should the contestant switch curtains or stick with the one that she has?To answer the question,determine the probability that she wins the prize if she switches. 1.4.31.A French nobleman,Chevalier de Méeré,had asked a famous mathematician,Pascal,to explain why the following two probabilities were different(the difference had been noted from playing the game many times):(1)at least one six in four independent casts of a six-sided die;(2)at least a pair of sixes in 24 independent casts of a pair of dice.From proportions it seemed to de Méré that the probabilities should be the same.Compute the probabilities of(1)and(2). 1.4.32.Hunters A and B shoot at a target;the probabilities of hitting the target are P1 and P2,respectively.Assuming independence,can P1 and P2 be selected so that P(zero hits)= P(one hit)= P(two hits)? 1.4.33.At the beginning of a study of individuals,15% were classified as heavy smokers,30% were classified as light smokers,and 55% were classified as nonsmokers.In the five-year study,it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers,respectively.A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker. 1.4.34.A chemist wishes to detect an impurity in a certain compound that she is making.There is a test that detects an impurity with probability 0.90;however,this test indicates that an impurity is there when it is not about 5% of the time.The chemist produces compounds with the impurity about 20% of the time.A compound is selected at random from the chemist's output.The test indicates that an impurity is present.What is the conditional probability that the compound actually has the impurity? 1.5 Random Variables The reader perceives that a sample space C may be tedious to describe if the elements of C are not numbers.We now discuss how we may formulate a rule,or a set of rules,by which the elements c of C may be represented by numbers.We begin the discussion with a very simple example.Let the random experiment be the toss of a coin and let the sample space associated with the experiment be C={H,T},where H and T represent heads and tails,respectively.Let X be a function such that X(T)=0 and X(H)=1.Thus X is a real-valued function defined on the sample space C which takes us from the sample space C to a space of real numbers D={0,1}.We now formulate the definition of a random variable and its space.
《数理统计学导论(英文版•第7版)》是数理统计方面的一本经典教材，自1959年出版以来，广受读者好评，并被众多院校选为教材，如布朗大学、乔治华盛顿大学等。第7版延续了前几版的一贯风格，清晰而全面地阐述了数理统计的基本理论，并且为了让读者更好地理解数理统计，还提供了丰富的例子和一些重要的背景材料。
“该书写作风格极其清晰，就更高等内容的应用而言，我没有任何质疑。书中内容表述专业而现代，假如我有机会再次讲授数理统计学，我会毫不犹豫使用它，同时推荐给我的同事们。” ——Walter Freiberger，布朗大学
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数理统计学导论（英文版数理统计学导论（英文版数理统计学导论（英文版
印刷好！书是经典！但是价格有些贵！想看一看国外的数理统计基础的教材！咬牙拿下！
之前读过第五版的Introduction To Mathematical Statistics，觉得挺不错的，但是在记号上面还是偏过时。这次第七版已经修正这种瑕疵（比如说，补集的记法）。学习这本书，还是觉得要把习题都给做了，现在学计量经济学，里面就有个结论是用到习题2.3.5的结果的。不过就是没有详细的Solution（英文版的Solution都不详细=。=，中文版的都是第四版的了，叫《数理统计学习题详解》），不大适合自学。这会不会是所有教材的通病呢？不过总而言之，还是值得一读的
这本数理统计学曾经被一位南亚同学大加赞赏，说他们国家的影印版不多，这是其中之一，呵呵。读过第五版，这个当做收藏了。
有点厚，但是内容很全。刚刚开始看，国外教材和国内的风格完全不一样。
正在阅读中，感觉由浅入深，比较清晰
还没看，准备当教材用的，朋友推荐
我是外行，等其评论后补上。如好，则不枉我的话费
有点难度，需要用心，呵呵。
看了一小半，谈谈自己的感受。本书没有从测度论的角度来描述概率，使得本书变得易读，但也成了本书的短板。本书从数理的角度讲统计，目录上看非常好且全面。但由于没有测度论，使得对某些定理的证明不够普遍性。例如本书用ChebyShev方法来证明弱大数定理，这个证明需要方差有限这个条件。作者经常非常不厚道的用by the law of Large Numbers来完成一些证明，等读者自己来推敲。最郁闷的是作者在应用的时候，使用的是对大数定律更高级的版本（根本不需要假设方差有限）。书没看完，不太好说，但目前感觉是本好书。
买这本书是冲着“mathematical”这个词和该书的内容比较全面（包含了em算法这类一般数统类书里没有的内容）这两点来的。安照美国那边命名的标准，冠以“mathematical”的统计学一般是偏于数学基础，然而在这本书中，这种数学基础没有体现出来。具体来讲，书中出现了partition、order（partial的）、Borel field等概念，然而作者并没有对这些概念进行定义，而是采用文字解说的形式，也就是所谓的rounding about；而这些rounding about有时会让人感到不知所云，有时还必须自行回忆相关概念的定义（注意：教材中并没有包含相关的概念），才知道作者想要表达的意思.....还不如直接给出定义更加简单明了、节省篇幅。
跟原版的页数都是对应的，比起原版教材，这个引进版值多了