數理統計（第2版）（英文版） [Mathematical Statistics(Second Edition)] epub pdf mobi txt 電子書 下載 2024

數理統計（第2版）（英文版） [Mathematical Statistics(Second Edition)] epub pdf mobi txt 電子書 下載 2024

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數理統計（第2版）（英文版） [Mathematical Statistics(Second Edition)] epub pdf mobi txt 電子書 下載 2024

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內容簡介

　　Probability Theory、Probability Spaces and Random Elements、σ－fields and measures、Measurable functions and distributions、Integration and Differentiation、Integration、Radon.Nikodym derivative、Distributions and Their Characteristics、Distributions and probability densities、Moments and moment inequalities、Moment generating and characteristic functions、onditional Expectations、Conditional expectations、Independence、Conditional distributions、Markov chains and martingales、Asymptotic Theory、Convergence modes and stochastic orders等等。

內頁插圖

目錄

Preface to the First Edition
Preface to the Second Edition
Chapter 1.Probability Theory
1.1 Probability Spaces and Random Elements
1.1.1σ－fields and measures
1.1.2 Measurable functions and distributions
1.2 Integration and Differentiation
1.2.1 Integration
1.2.2 Radon.Nikodym derivative
1.3 Distributions and Their Characteristics
1.3.1 Distributions and probability densities
1.3.2 Moments and moment inequalities
1.3.3 Moment generating and characteristic functions
1.4 Conditional Expectations
1.4.1 Conditional expectations
1.4.2 Independence
1.4.3 Conditional distributions
1.4.4 Markov chains and martingales
1.5 Asymptotic Theory
1.5.1 Convergence modes and stochastic orders
1.5.2 Weak convergence
1.5.3 Convergence of transformations
1.5.4 The law of large numbers
1.5.5 The central limit theorem
1.5.6 Edgeworth and Cornish-Fisher expansions
1.6 Exercises

Chapter 2. Fundamentals of Statistics
2.1 Populations，Samples，and Models
2.1.1 Populations and samples
2.1.2 Parametric and nonparametric models
2.1.3 Exponential and location.scale families
2.2 Statistics.Sufficiency，and Completeness
2.2.1 Statistics and their distributions
2.2.2 Sufficiency and minimal sufficiency
2.2.3 Complete statistics
2.3 Statistical Decision Theory
2.3.1 Decision rules，lOSS functions，and risks
2.3.2 Admissibility and optimality
2.4 Statistical Inference
2.4.1 P0il）t estimators
2.4.2 Hypothesis tests
2.4.3 Confidence sets
2.5 Asymptotic Criteria and Inference
2.5.1 Consistency
2.5.2 Asymptotic bias，variance，and mse
2.5.3 Asymptotic inference
2.6 Exercises

Chapter 3.Unbiased Estimation
3.1 The UMVUE
3.1.1 Sufficient and complete statistics
3.1.2 A necessary and.sufficient condition
3.1.3 Information inequality
3.1.4 Asymptotic properties of UMVUEs
3.2 U-Statistics
3.2.1 Some examples
3.2.2 Variances of U-statistics
3.2.3 The projection method
3.3 The LSE in Linear Models
3.3.1 The LSE and estimability
3.3.2 The UMVUE and BLUE
3.3.3 R0bustness of LSEs
3.3.4 Asymptotic properties of LSEs
3.4 Unbiased Estimators in Survey Problems
3.4.1 UMVUEs of population totals
3.4.2 Horvitz-Thompson estimators
3.5 Asymptotically Unbiased Estimators
3.5.1 Functions of unbiased estimators
3.5.2 The method ofmoments
3.5.3 V-statistics
3.5.4 The weighted LSE
3.6 Exercises

Chapter 4.Estimation in Parametric Models
4.1 Bayes Decisions and Estimators
4.1.1 Bayes actions
4.1.2 Empirical and hierarchical Bayes methods
4.1.3 Bayes rules and estimators
4.1.4 Markov chain Mollte Carlo
4.2 Invariance......
4.2.1 One-parameter location families
4.2.2 One-parameter seale families
4.2.3 General location-scale families
4.3 Minimaxity and Admissibility
4.3.1 Estimators with constant risks
4.3.2 Results in one-parameter exponential families
4.3.3 Simultaneous estimation and shrinkage estimators
4.4 The Method of Maximum Likelihood
4.4.1 The likelihood function and MLEs
4.4.2 MLEs in generalized linear models
4.4.3 Quasi-likelihoods and conditional likelihoods
4.5 Asymptotically Efficient Estimation
4.5.1 Asymptotic optimality
4.5.2 Asymptotic efficiency of MLEs and RLEs
4.5.3 Other asymptotically efficient estimators
4.6 Exercises

Chapter 5.Estimation in Nonparametric Models
5.1 Distribution Estimators
5.1.1 Empirical C.d.f.s in i.i.d.cases
5.1.2 Empirical likelihoods
5.1.3 Density estimation
5.1.4 Semi-parametric methods
5.2 Statistical Functionals
5.2.1 Differentiability and asymptotic normality
5.2.2 L-.M-.and R-estimators and rank statistics
5.3 Linear Functions of Order Statistics
5.3.1 Sample quantiles
5.3.2 R0bustness and efficiency
5.3.3 L-estimators in linear models
5.4 Generalized Estimating Equations
5.4.1 The GEE method and its relationship with others
5.4.2 Consistency of GEE estimators
5.4.3 Asymptotic normality of GEE estimators
5.5 Variance Estimation
5.5.1 The substitution.method
5.5.2 The jackknife
5.5.3 The bootstrap
5.6 Exercises

Chapter 6.Hypothesis Tests
6.1 UMP Tests
6.1.1 The Neyman-Pearson lemma
6.1.2 Monotone likelihood ratio
6.1.3 UMP tests for two-sided hypotheses
6.2 UMP Unbiased Tests
6.2.1 Unbiasedness，similarity，and Neyman structure
6.2.2 UMPU tests in exponential families
6.2.3 UMPU tests in normal families
……
Chapter 7 Confidence Sets
References
List of Notation
List of Abbreviations
Index of Definitions，Main Results，and Examples
Author Index
Subject Index

前言/序言

　　This book is intended for a course entitled Mathematical Statistics offered at the Department of Statistics，University of Wisconsin．Madison．This course，taught in a mathematically rigorous fashion，covers essential materials in statistical theory that a first or second year graduate student typicallY needs to learn as preparation for work on a Ph．D．degree in statistics．The course is designed for two 15-week semesters．with three lecture hours and two discussion hours in each week. Students in this course are assumed to have a good knowledge of advanced calgulus．A course in real analy．sis or measure theory prior to this course is often recommended．Chapter 1 provides a quick overview of important concepts and results in measure-theoretic probability theory that are used as tools in mathematical statistics．Chapter 2 introduces some fundamental concepts in statistics，including statistical models．the principle of SUfIlciency in data reduction，and two statistical approaches adopted throughout the book： statistical decision theory and statistical inference．
　　Each of Chapters 3 through 7 provides a detailed study of an important topic in statistical decision theory and inference：Chapter 3 introduces the theory of unbiased estimation；Chapter 4 studies theory and methods in point estimation ander parametric models；Chapter 5 covers point estimation in nonparametric settings；Chapter 6 focuses on hypothesis testing；and Chapter 7 discusses interval estimation and confidence sets．The classical frequentist approach is adopted in this book．although the Bayesian approach is also introduced (§2．3．2，§4．1，§6．4．4，and§7．1．3)．Asymptotic(1arge sample)theory，a crucial part of statistical inference，is studied throughout the book，rather than in a separate chapter．
　　About 85％of the book covers classical results in statistical theory that are typically found in textbooks of a similar level．These materials are in the Statistics Department’S Ph．D．qualifying examination syllabus．

數理統計（第2版）（英文版） [Mathematical Statistics(Second Edition)] epub pdf mobi txt 電子書 下載 2024

數理統計（第2版）（英文版） [Mathematical Statistics(Second Edition)] 下載 epub mobi pdf txt 電子書

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Probability Theory、Probability Spaces and Random Elements、σ－fields and measures、Measurable functions and distributions、Integration and Differentiation、Integration、Radon.Nikodym derivative、Distributions and Their Characteristics、Distributions and probability densities、Moments and moment inequalities、Moment generating and characteristic functions、onditional Expectations、Conditional expectations、Independence、Conditional distributions、Markov chains and martingales、Asymptotic Theory、Convergence modes

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譯者序前言第1章 概率1 1.1 引言1 1.2 樣本空間1 1.3 概率測度3 1.4 概率計算：計數方法5 1.4.1 乘法原理 6 1.4.2 排列與組閤 7 1.5 條件概率12 1.6 獨立性17 1.7 結束語19 1.8 習題20第2章 隨機變量26 2.1 離散隨機變量26 2.1.1 伯努利隨機變量27 2.1.2 二項分布28 2.1.3 幾何分布和負二項分布29 2.1.4 超幾何分布 30 2.1.5 泊鬆分布31 2.2 連續隨機變量34 2.2.1 指數密度36 2.2.2 伽馬密度38 2.2.3 正態分布39 2.2.4 貝塔密度41 2.3 隨機變量的函數42 2.4 結束語45 2.5 習題46第3章 聯閤分布51 3.1 引言51 3.2 離散隨機變量52 3.3 連續隨機變量53 3.4 獨立隨機變量60 3.5 條件分布61 3.5.1 離散情形61 3.5.2 連續情形62 3.6 聯閤分布隨機變量函數67 3.6.1 和與商68 3.6.2 一般情形70 3.7 極值和順序統計量73 3.8 習題75第4章 期望82 4.1 隨機變量的期望82 4.1.1 隨機變量函數的期望85 4.1.2 隨機變量綫性組閤的期望 87 4.2 方差和標準差91 4.2.1 測量誤差模型94 4.3 協方差和相關96 4.4 條件期望和預測102 4.4.1 定義和例子102 4.4.2 預測106 4.5 矩生成函數108 4.6 近似方法112 4.7 習題116第5章 極限定理123 5.1 引言123 5.2 大數定律123 5.3 依分布收斂和中心極限定理125 5.4 習題130第6章 正態分布的導齣分布133 6.1 引言133 6.2 x2分布、t分布和F分布 133 6.3 樣本均值和樣本方差134 6.4 習題136第7章 抽樣調查138 7.1 引言138 7.2 總體參數138 7.3 簡單隨機抽樣140 7.3.1 樣本均值的期望和方差140 7.3.2 總體方差的估計 145 7.3.3 X 抽樣分布的正態近似 148 7.4 比率估計152 7.5 分層隨機抽樣157 7.5.1 引言和記號157 7.5.2 分層估計的性質 157 7.5.3 分配方法 160 7.6 結束語163 7.7 習題164第8章 參數估計和概率分布擬閤176 8.1 引言176 8.2 粒子排放量的泊鬆分布擬閤176 8.3 參數估計177 8.4 矩方法179 8.5 最大似然方法184 8.5.1 多項單元概率的最大似然估計187 8.5.2 最大似然估計的大樣本理論189 8.5.3 最大似然估計的置信區間 193 8.6 參數估計的貝葉斯方法197 8.6.1 先驗的進一步注釋204 8.6.2 後驗的大樣本正態近似205 8.6.3 計算問題 206 8.7 效率和剋拉默{拉奧下界207 8.7.1 例子：負二項分布210 8.8 充分性212 8.8.1 因子分解定理212 8.8.2 拉奧{布萊剋韋爾定理215 8.9 結束語216 8.10 習題217第9章 假設檢驗和擬閤優度評估228 9.1 引言228 9.2 奈曼{皮爾遜範式229 9.2.1 顯著性水平的設定和p 值概念 232 9.2.2 原假設232 9.2.3 一緻最優勢檢驗 233 9.3 置信區間和假設檢驗的對偶性233 9.4 廣義似然比檢驗235 9.5 多項分布的似然比檢驗236 9.6 泊鬆散布度檢驗240 9.7 懸掛根圖242 9.8 概率圖244 9.9 正態性檢驗248 9.10 結束語249 9.11 習題250第10章 數據匯總260 10.1 引言260 10.2 基於纍積分布函數的方法 260 10.2.1 經驗纍積分布函數 260 10.2.2 生存函數262 10.2.3 分位數{分位數圖266 10.3 直方圖、密度麯綫和莖葉圖268 10.4 位置度量270 10.4.1 算術平均271 10.4.2 中位數 272 10.4.3 截尾均值274 10.4.4 M 估計274 10.4.5 位置估計的比較275 10.4.6 自助法評估位置度量的變異性 275 10.5 散度度量277 10.6 箱形圖278 10.7 利用散點圖探索關係279 10.8 結束語281 10.9 習題281第11章 兩樣本比較 289 11.1 引言289 11.2 兩獨立樣本比較289 11.2.1 基於正態分布的方法289 11.2.2 勢298 11.2.3 非參數方法：曼恩{惠特尼檢驗299 11.2.4 貝葉斯方法305 11.3 配對樣本比較306 11.3.1 基於正態分布的方法307 11.3.2 非參數方法：符號秩檢驗308 11.3.3 例子：測量魚的汞水平310 11.4 試驗設計311 11.4.1 乳腺動脈結紮術311 11.4.2 安慰劑效應312 11.4.3 拉納剋郡牛奶試驗 312 11.4.4 門腔分術313 11.4.5 FD&C Red No.40313 11.4.6 關於隨機化的進一步評注314 11.4.7 研究生招生的觀測研究、混雜和偏見315 11.4.8 審前調查315 11.5 結束語316 11.6 習題317第12章 方差分析328 12.1 引言328 12.2 單因子試驗設計328 12.2.1 正態理論和 F 檢驗329 12.2.2 多重比較問題 333 12.2.3 非參數方法：剋魯斯卡爾{沃利斯檢驗335 12.3 二因子試驗設計336 12.3.1 可加性參數化 337 12.3.2 二因子試驗設計的正態理論339 12.3.3 隨機化區組設計344 12.3.4 非參數方法：弗裏德曼檢驗346 12.4 結束語347 12.5 習題348第13章 分類數據分析354 13.1 引言354 13.2 費捨爾精確檢驗354 13.3 卡方齊性檢驗355 13.4 卡方獨立性檢驗358 13.5 配對設計360 13.6 優勢比362 13.7 結束語36

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