Fundamental Statistical Inference : A Computational Approach (Hardcover)

A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field

This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided.

The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. 

Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs. 

一本關於統計推論的實踐性手冊，涵蓋了這個不斷發展的領域的最新進展。

這本為初級研究生提供的清晰易懂的書籍，以實用和詳細的方式介紹了統計推論領域，提供了完整的結果推導、討論和用於計算的MATLAB程式。它強調材料的相關性細節、直覺和討論，並以非常現代的統計推論為視角。除了與數學統計學相關的經典主題外，還包括對置信區間計算的直觀介紹（單一和雙重自助法）、收縮估計、尾部（極大矩）估計以及除了最大概似估計之外的各種點估計方法，包括使用特徵函數和間接推論。書中提供了所有方法的實際例子。詳細介紹了與離散混合正態分佈相關的估計問題及其解決方案。全書非常強調非高斯分佈，包括使用穩定帕雷托分佈和快速計算非中心學生t分佈的細節。整章專門介紹了優化，包括基於Hessian的方法的發展，以及不需要連續性的啟發式/遺傳算法，並提供了MATLAB程式碼。

本書既包含理論又包含非技術性的討論，並且在文獻方面提供了大量參考，重點放在替代的、更現代的方法上。書中討論了關於假設檢驗和p值在模型選擇中誤用的最新文獻，並強調了替代的模型選擇方法，儘管對於分佈假設的假設檢驗進行了詳細介紹，特別是對於正態分佈。

本書分為三個部分：統計學的基本概念；進一步的基本概念；以及其他主題。《基本統計推論：一種計算方法》的全面章節包括：點估計和區間估計的介紹；適合度檢驗和假設檢驗；概然估計；數值優化；點估計方法；Q-Q圖和分佈檢驗；無偏點估計和偏差減少；分析區間估計；重尾情境下的推論；間接推論方法；以及作為附錄的概率論基本概念回顧，後者使本書自成一體，並提供了一些高級主題的材料，如鞍點近似、金融中的預期損失、穩定帕雷托分佈的計算以及收斂定理和證明。