数理统计学导论

基本信息

• 商品名称：数理统计学导论（英文版·原书第8版）
• 作者：[美]罗伯特 V. 霍格(Robert V. Hogg)等
• 定价：149
• 出版社：机械工业
• 书号：9787111670322

其他参考信息（以实物为准）

• 出版时间：2021-01-01
• 印刷时间：2021-01-01
• 版次：1
• 印次：1
• 开本：
• 包装：平装
• 页数：746

编辑推荐语

本书是数理统计方面的经典教材，自1959年 版出版以来，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8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 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。与前几版相比，本版包含了 多的真实数据集，扩展了统计软件R的使用。

内容提要

本书是数理统计方面的经典教材，从数理统计学的初级基本概念及原理开始，详细讲解概率与分布、多元分布、特殊分布、统计推断基础、极大似然法等内容，并且涵盖一些 主题，如一致性与极限分布、充分性、 优假设检验、正态模型的推断、非参数与稳健统计、贝叶斯统计等.此外，为了帮助读者 好地理解数理统计和巩固所学知识，书中还提供了一些重要的背景材料、大量实例和习题.
本书可以作为高等院校数理统计相关课程的教材，也可供相关专业人员参考使用.

作者简介

罗伯特·V. 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。他曾担任美国统计学会（ASA），获得过包括美国数学学会杰出教育奖在内的多项教学奖。

约瑟夫·W. 麦基恩（Joseph W. McKean） 西密歇根大学统计系教授，美国统计学会会士。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。

艾伦·T. 克雷格（Allen T. Craig） 艾奥瓦大学教授，已于1970年退休。他曾担任 数理统计学会（IMS） 任秘书长，发起并参与了本书的撰写工作。

目录

第1章　概率与分布1
1.1　引论1
1.2　集合3
1.2.1　回顾集合论4
1.2.2　集合函数7
1.3　概率集函数12
1.3.1　计数规则16
1.3.2　概率的附加性质18
1.4　条件概率与独立性23
1.4.1　独立性28
1.4.2　模拟31
1.5　随机变量37
1.6　离散随机变量45
1.6.1　变量变换47
1.7　连续随机变量49
1.7.1　分位数51
1.7.2　变量变换53
1.7.3　混合离散型和连续型分布56
1.8　随机变量的期望60
1.8.1　用R计算期望增益估计65
1.9　某些特殊期望68
1.10　重要不等式78
第2章　多元分布85
2.1　二元随机变量的分布85
2.1.1　边际分布89
2.1.2　期望93
2.2　二元随机变量变换100
2.3　条件分布与期望109
2.4　独立随机变量117
2.5　相关系数125
2.6　推广到多个随机变量134
*2.6.1　多元方差–协方差矩阵140
2.7　多个随机向量的变换143
2.8　随机变量的线性组合151
第3章　某些特殊分布155
3.1　二项分布及有关分布155
3.1.1　负二项分布和几何分布159
3.1.2　多正态分布160
3.1.3　超几何分布162
3.2　泊松分布167
3.3　、2以及分布173
3.3.1　2分布178
3.3.2　分布180
3.4　正态分布186
*3.4.1　污染正态分布193
3.5　多元正态分布198
3.5.1　二元正态分布198
*3.5.2　多元正态分布的一般情况199
*3.5.3　应用206
3.6　t分布与F分布210
3.6.1　t分布210
3.6.2　F分布212
3.6.3　学生定理214
*3.7　混合分布218
第4章　基本统计推断225
4.1　抽样与统计量225
4.1.1　点估计226
4.1.2　pmf与pdf的直方图估计230
4.2　置信区间238
4.2.1　均值之差的置信区间241
4.2.2　比例之差的置信区间243
*4.3　离散分布参数的置信区间248
4.4　次序统计量253
4.4.1　分位数257
4.4.2　分位数置信区间261
4.5　假设检验介绍267
4.6　统计检验的深入研究275
4.6.1　观测的显著性水平：p值279
4.7　卡方检验283
4.8　蒙特卡罗方法292
4.8.1　筛选生成算法298
4.9　自助法303
4.9.1　百分位数自助置信区间303
4.9.2　自助检验法308
*4.10　分布容许限315
第5章　一致性与极限分布321
5.1　依概率收敛321
5.1.1　抽样和统计量324
5.2　依分布收敛327
5.2.1　概率有界333
5.2.2　Δ方法334
5.2.3　矩母函数方法336
5.3　中心极限定理341
*5.4　推广到多元分布348
第6章　极大似然法355
6.1　极大似然估计355
6.2　拉奥–克拉默下界与有效性362
6.3　极大似然检验376
6.4　多参数估计386
6.5　多参数检验395
6.6　EM算法404
第7章　充分性413
7.1　估计量品质的测量413
7.2　参数的充分统计量419
7.3　充分统计量的性质426
7.4　完备性与 性430
7.5　指数分布类435
7.6　参数的函数440
7.6.1　自助标准误差444
7.7　多参数的情况447
7.8　 小充分性与从属统计量454
7.9　充分性、完备性以及独立性461
第8章　 优假设检验469
8.1　 大功效检验469
8.2　一致 大功效检验479
8.3　似然比检验487
8.3.1　正态分布均值的似然比检验488
8.3.2　正态分布方差的似然比检验495
*8.4　序贯概率比检验500
*8.5　极小化极大与分类方法507
8.5.1　极小化极大方法507
8.5.2　分类510
第9章　正态线性模型的推断515
9.1　介绍515
9.2　单向方差分析516
9.3　非中心2分布与F分布522
9.4　多重比较法525
9.5　双向方差分析531
9.5.1　因子间的相互作用534
9.6　回归问题539
9.6.1　极大似然估计540
*9.6.2　 小二乘拟合的几何解释546
9.7　独立性检验551
9.8　某些二次型的分布555
9.9　某些二次型的独立性562
0章　非参数与稳健统计学569
10.1　位置模型569
10.2　样本中位数与符号检验572
10.2.1　渐近相对有效性577
10.2.2　基于符号检验的估计方程582
10.2.3　中位数置信区间584
10.3　威尔科克森符号秩586
10.3.1　渐近相对有效性591
10.3.2　基于威尔科克森符号秩的估计方程593
10.3.3　中位数置信区间594
10.3.4　蒙特卡罗调查595
10.4　曼–惠特尼–威尔科克森方法598
10.4.1　渐近相对有效性602
10.4.2　基于MWW的估计方程604
10.4.3　移位参数Δ的置信区间604
10.4.4　功效函数的蒙特卡罗调查605
*10.5　一般秩得分607
10.5.1　效力610
10.5.2　基于一般得分的估计方程612
10.5.3　 优化： 佳估计612
*10.6　适应方法619
10.7　简单线性模型625
10.8　测量关联性631
10.8.1　肯德尔631
10.8.2　斯皮尔曼634
10.9　稳健概念638
10.9.1　位置模型638
10.9.2　线性模型645
1章　贝叶斯统计655
11.1　贝叶斯方法655
11.1.1　先验分布与后验分布656
11.1.2　贝叶斯点估计658
11.1.3　贝叶斯区间估计662
11.1.4　贝叶斯检验方法663
11.1.5　贝叶斯序贯方法664
11.2　其他贝叶斯术语及思想666
11.3　吉布斯抽样器672
11.4　现代贝叶斯方法679
11.4.1　经验贝叶斯682
附录A　数学687
附录B　R入门693
附录C　常用分布列表703
附录D　分布表707
附录E　参考文献715
附录F　部分习题答案721
索引733



Contents
1 Probability and Distributions ....................................1
1.2 Sets....................................3
1.2.1 Review of SetTheory......................4
1.2.2 Set Functions...........................7
1.3 The Probability SetFunction......................12
1.3.1 Counting Rules..........................16
1.3.2 Additional Properties of Probability..............18
1.4 Conditional Probability and Indepen dence...............23
1.4.1 Independence...........................28
1.4.2 Simulations............................31
1.5 Random Variables............................37
1.6 Discrete Random Variables.......................45
1.6.1 Transformations.........................47
1.7 Continuous Random Variables.....................49
1.7.1 Quantiles.............................51
1.7.2 Transformations.........................53
1.7.3 Mixtures of Discrete and Continuous Type Distributions...56
1.8 Expectation of a Random Variable...................60
1.8.1 R Computation for an Estimation of the Expected Gain...65
1.9 Some Special Expectations.......................68
1.10 Important Inequalities..........................78
2 Multivariate Distributions 85
2.1 Distributions of Two Random Variables................85
2.1.1 Marginal Distributions......................89
2.1.2 Expectation............................93
2.2 Transformations: Bivariate Random Variables.............100
2.3 Conditional Distributions and Expectations..............109
2.4 Independent Random Variables.....................117
2.5 The Correlation Coefficient.......................125
2.6 Extension to Several Random Variables................134
2.6.1 *Multivariate Variance-Covariance Matrix...........140
2.7 Transformations for Several Random Variables............143
2.8 Linear Combinations of Random Variables...............151
3 Some Special Distributions 155
3.1 The Binomial and Related Distributions................155
3.1.1 Negative Binomial and Geometric Distributions........159
3.1.2 Multinomial Distribution....................160
3.1.3 Hypergeometric Distribution..................162
3.2 The Poisson Distribution........................167
3.3 TheΓ,χ2,andβDistributions.....................173
3.3.1 Theχ2-Distribution.......................178
3.3.2 The β-Distribution........................180
3.4 The Normal Distribution.........................186
3.4.1 *Contaminated Normals.....................193
3.5 The Multivariate Normal Distribution.................198
3.5.1 Bivariate Normal Distribution..................198
3.5.2 *Multivariate Normal Distribution, General Case.......199
3.5.3 *Applications...........................206
3.6 t- and F- Distributions..........................210
3.6.1 The t- distribution........................210
3.6.2 The F- distribution........................212
3.6.3 Student’s Theorem........................214
3.7 *Mixture Distributions..........................218
4 Some Elementary Statistical Inferences 225
4.1 Sampling and Statistics.........................225
4.1.1 Point Estimators.........................226
4.1.2 Histogram Estimates of pmfs and pdfs.............230
4.2 ConfidenceIntervals...........................238
4.2.1 Confidence Intervals for Differencein Means..........241
4.2.2 Confidence Interval for Differencein Proportions.......243
4.3 *Confidence Intervals for Parameters of Discrete Distributions....248
4.4 Order Statistics..............................253
4.4.1 Quantiles.............................257
4.4.2 Confidence Intervals for Quantiles...............261
4.5 Introduction to Hypothesis Testing...................267
4.6 Additional Comments About Statistical Tests.............275
4.6.1 Observed Significance Level, p-value..............279
4.7 Chi-Square Tests.............................283
4.8 The Method of Monte Carlo.......................292
4.8.1 Accept–Reject Generation Algorithm..............298
4.9 Bootstrap Procedures..........................303
4.9.1 Percentile Bootstrap Confidence Intervals...........303
4.9.2 Bootstrap Testing Procedures..................308
4.10 *Tolerance Limits for Distributions...................315
5 Consistency and Limiting Distributions 321
5.1 Convergence in Probability.......................321
5.1.1S ampling and Statistics.....................324
5.2 Convergence in Distribution.......................327
5.2.1 Bounded in Probability.....................333
5.2.2 Δ-Method.............................334
5.2.3 Moment Generating Function Technique............336
5.3 Central Limit Theorem.........................341
5.4 *Extensions to Multivariate Distributions...............348
6 Maximum Likelihood Methods 355
6.1 Maximum Likelihood Estimation....................355
6.2 Rao–Cramer Lower Bound and Effciency...............362
6.3 Maximum Likelihood Tests.......................376
6.4 Multiparameter Case: Estimation....................386
6.5 Multiparameter Case: Testing......................395
6.6 The EM Algorithm............................404
7 Sufficiency 413
7.1 Measures of Quality of Estimators...................413
7.2 A Sufficient Statistic for a Parameter..................419
7.3 Properties of a Sufficient Statistic....................426
7.4 Completeness and Uniqueness......................430
7.5 The Exponential Class of Distributions.................435
7.6 Functions of a Parameter........................440
7.6.1 Bootstrap Standard Errors...................444
7.7 The Case of Several Parameters.....................447
7.8 Minimal Sufficiency and Ancillary Statistics..............454
7.9 Sufficiency, Completeness, and Independence.............461
8 Optimal Tests of Hypotheses 469
8.1 Most Powerful Tests...........................469
8.2 Uniformly Most Powerful Tests.....................479
8.3 Likelihood Ratio Tests..........................487
8.3.1 Likelihood Ratio Tests for Testing Means of Normal Distributions..............................488
8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions.............................495
8.4 *The Sequential Probability Ratio Test.................500
8.5 *Minimax and Classification Procedures................507
8.5.1 Minimax Procedures.......................507
8.5.2 Classification...........................510
9 Inferences About Normal Linear Models 515
9.1 Introduction................................515
9.2 One-Way ANOVA............................516
9.3 Noncentralχ2 and F-Distributions...................522
9.4 Multiple Comparisons..........................525
9.5 Two-Way ANOVA............................531
9.5.1 Interaction between Factors...................534
9.6 A Regression Problem..........................539
9.6.1 Maximum Likelihood Estimates.................540
9.6.2 *Geometry of the Least Squares Fit..............546
9.7 A Test of Independence.........................551
9.8 The Distributions of Certain Quadratic Forms.............555
9.9 The Independence of Certain Quadratic Forms............562
10 Nonparametric and Robust Statistics 569
10.1 Location Models.............................569
10.2 Sample Median and the Sign Test....................572
10.2.1 Asymptotic Relative Efficiency.................577
10.2.2 Estimating Equations Basedonthe Sign Test.........582
10.2.3 Confidence Interval for the Median...............584
10.3 Signed-Rank Wilcoxon..........................586
10.3.1 Asymptotic Relative Efficiency.................591
10.3.2 Estimating Equations Basedon Signed-Rank Wilcoxon...593
10.3.3 Confidence Interval for the Median...............594
10.3.4 Monte Carlo Investigation....................595
10.4 Mann–Whitney–Wilcoxon Procedure..................598
10.4.1 Asymptotic Relative Efficiency.................602
10.4.2 Estimating Equations Basedon the Mann–Whitney–Wilcoxon 604
10.4.3 Confidence Interval for the Shift ParameterΔ.........604
10.4.4 Monte Carlo Investigation of Power..............605
10.5 *General RankScores..........................607
10.5.1 Efficacy..............................610
10.5.2 Estimating Equations Based on General Scores........612
10.5.3 Optimizati on: Best Estimates..................612
10.6 *Adaptive Procedures..........................619
10.7 Simple Linear Model...........................625
10.8 Measures of Association.........................631
10.8.1 Kendall’sτ............................631
10.8.2 Spearman’s Rho.........................634
10.9 Robust Concepts.............................638
10.9.1 Location Model..........................638
10.9.2 Linear Model...........................645
11 Bayesian Statistics 655
11.1 Bayesian Procedures...........................655
11.1.1 Prior and Posterior Distributions................656
11.1.2 Bayesian Point Estimation...................658
11.1.3 Bayesian Interval Estimation..................662
11.1.4 Bayesian Testing Procedures..................663
11.1.5 Bayesian Sequential Procedures.................664
11.2 More Bayesian Terminology and Ideas.................666
11.3 Gibbs Sampler..............................672
11.4 Modern Bayesian Methods........................679
11.4.1 Empirical Bayes.........................682
A Mathematical Comments 687
A.1 Regularity Conditions..........................687
A.2 Sequences.................................688
B R Primer 693
B.1 Basics...................................693
B.2 Probability Distributions.........................696
B.3 R Functions................................698
B.4 Loops...................................699
B.5 Inputand Output............................700
B.6 Packages..................................700
C Lists of Common Distributions 703
D Tables of Distributions 707
E References 715
F Answers to Selected Exercises 721
Index 733