数学与金融经典教材：统计理论（影印版） [Theory of Statistics] 下载 mobi epub pdf 电子书 2024

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　　After a brief review of elementary statistical theory， the coverage of thesubject matter begins with a detailed treatment of parametric statisticalmodels as motivated by DeFinetti's representation theorem for exchangeablerandom variables （Chapter l）. In addition， Dirichlet processes and othertailfree processes are presented as examples of infinite-dimensional param-eters. Chapter 2 introduces sufficient statistics from both Bayesian andnon-Bayesian viewpoints. Exponential families are discussed here becauseof the important role sufficiency plays in these models. Also， the conceptof iriformation is introduced together with its relationship to sufficiency.A representation theorem is given for general distributions based on suffi-cient statistics. Decision theory is the subject of Chapter 3， which includesdiscussions of admissibility and minimaxity. Section 3.3 presents an ax-iomatic derivation of Bayesian decision theory， including the use of condi-tional probability. Chapter 4 covers hypothesis testing， including unbiasedtests， P-values， and Bayes factors. We highlight the contrasts between thetraditional "uniformly most powerful" （UMP） approach to testing and de-cision theoretic approaches （both Bayesian and classical）. In particular， wesee how the asymmetric treatment of hypotheses and alternatives in theUMP approach accounts for much of the difference. Point and set estima-tion are the topics of Chapter 5. This includes unbiased and maximum like-lihood estimation as well as confidence， prediction， and tolerance sets. Wealso introduce robust estimation and the bootstrap. Equivariant decisionrules are covered in Chapter 6. In Section 6.2.2， we debunk the commonmisconception of equivariant rules as means for preserving decisions un-der changes of measurement scale. Large sample theory is the subject ofChapter 7. This includes asymptotic properties of sample quantiles， maxi-mum likelihood estimators， robust estimators， and posterior distributions.The last two chapters cover situations in which the random variables are
　　not modeled as being exchangeable. Hierarchical models （Chapter 8） areuseful for data arrays. Here， the parameters of the model can be modeled as exchangeable while the observables are only partially exchangeable. We introduce the popular computational tool known as Markov chain MonteOarlo， Gibbs sampling， or successive substitution sampling， which is very useful for fitting hierarchical models. Some topics in sequential analysis are presented in Chapter 9. These include classical tests， Bayesian decisions， confidence sets， and the issue of sampling to a foregone conclusion.

内容简介

　　《数学与金融经典教材：统计理论（影印版）》是一部经典的讲述统计理论的研究生教程，综合性强，内容涵盖：估计；检验；大样本理论，这些都是研究生要进入博士或者更高层次必须学习的预备知识。为了让读者具备更加强硬的数学背景和更广阔的理论知识，书中不仅给出了经典方法，也给出了贝叶斯推理知识。目次：概率模型；充分统计量；决策理论；假设检验；估计；等价；大样本理论；分层模型；序列分析；附录：测度与积分理论；概率论；数学定理；分布概述。
　　《数学与金融经典教材：统计理论（影印版）》读者对象：概率统计、数学专业以及相关专业的高年级本科生、研究生和相关的科研人员。

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目录

Preface

Chapter 1: Probability Models
1.1 Background
1.1.1 General Concepts
1.1.2 Classical Statistics
1.1.3 Bayesian Statistics
1.2 Exchangeability
1.2.1 Distributional Symmetry
1.2.2 Frequency and Exchangeability
1.3 Parametric Models
1.3.1 Prior, Posterior, and Predictive Distributions
1.3.2 Improper Prior Distributions
1.3.3 Choosing Probability Distributions
1.4 DeFinetti's Representation Theorem
1.4.1 Understanding the Theorems
1.4.2 The Mathematical Statements
1.5 Proofs of DeFinetti's Theorem and Related Results
1.5.1 Strong Law of Large Numbers
1.5.2 The Bernoulli Case
1.5.3 The General Finite Case
1.5.4 The General Infinite Case
1.5.5 Formal Introduction to Parametric Models
1.6 Infinite-Dimensional Parameters
1.6.1 Dirichlet Processes
1.6.2 Tailfree Processes

Chapter 2: Sufflcient Statistics
2.1.1 Notational Overview
2.1.3 Minimal and Complete Sufficiency
2.1.4 Ancillarity
2.2 Exponential Families of Distributions
2.2.1 Basic Properties
2.2.2 Smoothness Properties
2.2.3 A Characterization Theorem
2.3.1 Fisher Information
2.3.2 Kullback-Leibler Information
2.3.3 Conditional Information
2.4 Extremal Families
2.4.1 The Main Results
2.4.2 Examples

Chapter 3: Decision Theory
3.1 Decision Problems
3.1.2 Elements of Bayesian Decision Theory
3.1.3 Elements of Classical Decision Theory
3.1.4 Summary
3.2 Classical Decision Theory
3.2.1 The Role of Sufficient Statistics
3.2.2 Admissibility
3.2.3 James-Stein Estimators
3.2.5 Complete Classes
3.3 Axiomatic Derivation of Decision Theory
3.3.1 Definitions and Axioms
3.3.2 Examples
3.3.3 The Main Theorems
3.3.4 Relation to Decision Theory
3.3.5 Proofs of the Main Theorems
3.3.6 State-Dependent Utility

Chapter 4: Hypothesis Testing
4.1 Introduction
4.1.1 A Special Kind of Decision Problem
4.1.2 Pure Significance Tests
4.2 Bayesian Solutions
4.2.1 Testing in General
4.2.2 Bayes Factors
4.3 Most Powerful Tests
4.3.1 Simple Hypotheses and Alternatives
4.3.2 Simple Hypotheses, Composite Alternatives
4.3.3 0ne-Sided Tests
4.3.4 Two-Sided Hypotheses
4.4 Unbiased Tests
4.4.1 General Results

Chapter 5: E8timation
Chapter 6: Equivariance
Chapter 7: Large Sample Theory
Chapter 8: Hierarchical Models
chapter 9: sequential analysis

appendix a: measure and integration theory
appendix b: probability theory
appendix c: mathematical theorems not proven here
appendix d: summary of distributions
references
notation and abbreviation index
name index
subject index

前言/序言

数学与金融经典教材：统计理论（影印版） [Theory of Statistics] 下载 mobi epub pdf txt 电子书 格式

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这是一本关于金融数学方面的书籍，我非常喜欢。金融数学（Financial Mathematics），又称分析金融学、数理金融学、数学金融学，是20世纪80年代末、90年代初兴起的数学与金融学的交叉学科。金融数学主要运用现代数学理论和方法(如:随机分析、随机最优控制、组合分析、非线性分析、多元统计分析、数学规划、现代计算方法等)对金融(除银行功能之外,还包括投资、债券、基金、股票、期货、期权等金融工具和市场)的理论和实践进行数量的分析研究。其核心问题是不确定条件下的最优投资策略的选择理论和资产的定价理论。套利,最优和均衡是其中三个主要概念。近二十几年来，金融数学不仅对金融工具的创新和对金融市场的有效运作产生直接的影响，而且对公司的投资决策和对研究开发项目的评估(如实物期权)以及在金融机构的风险管理中得到广泛应用。金融与数学的结合越来越引起国际金融界和数学界的关注。金融数学也已经开始在我国得到了越来越广泛的重视。所以更应鼓励数学系学生去考经济金融研究生；增加经济和金融专业数学内容(而不是减少)，鼓励专家学者“下海”，以形成高素质的新型企业家、银行家集团，为我国的金融体制改革，以及我国金融市场与国际金融市场接轨、参与国际金融市场竞争，做出应有的贡献。

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