Asymptotic Statistical Inference: A Basic Course Using R
暫譯: 漸近統計推斷：使用 R 的基礎課程

Deshmukh, Shailaja, Kulkarni, Madhuri

Asymptotic Statistical Inference: A Basic Course Using R

買這商品的人也買了...

相關主題

商品描述

The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical.

Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts.

The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators andcarrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book.

The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.

商品描述(中文翻譯)

本書介紹了漸近統計推斷理論的基本概念，詳細闡述了一些基本的大樣本最佳性質的估計量及一些檢定程序。討論了估計量一致性及其大樣本分佈的最理想特性，並進行適當的標準化，重點在於一致且漸近正態（CAN）估計量。顯示對於屬於指數族和克拉美族的機率模型，指數參數的最大似然估計量是CAN。本書描述了一些大樣本檢定程序，特別是最常用的似然比檢定程序。當基礎機率模型為多項分佈時，涉及了似然比檢定程序的各種應用，包括適合度檢定和列聯表檢定。本書還討論了得分檢定和瓦爾德檢定，及其與似然比檢定和卡爾·皮爾遜的卡方檢定的關係。一個重要的發現是，在檢定有關多項分佈參數的任何假設時，得分檢定統計量和卡爾·皮爾遜的卡方檢定統計量是相同的。

本書包含了多個不同難度的示例，以澄清概念。為了更好地理解這些概念，每章都包含了各種練習題。幾乎所有練習題的解答都在最後一章中提供，以激勵學生解決這些練習題並幫助消化基礎概念。

漸近推斷的概念在現代統計中至關重要，但由於其抽象性質，難以掌握。為了克服這一困難，跟上使用R軟體進行統計計算的最新趨勢，本書廣泛使用R軟體來說明概念、驗證估計量的性質以及執行各種檢定程序。每章的最後部分提供R代碼，以揭示和直觀展示不同概念和程序的隱藏方面。將理論與R軟體相結合是本書的一個新穎且獨特的特點。

本書主要設計為研究生課程中漸近統計推斷的單學期入門教材，如統計學、生物統計學或計量經濟學。它還將提供足夠的背景信息，以便學習隨機過程中的推斷。本書將滿足對一本簡明但清晰且對學生友好的書籍的需求，從概念和計算上介紹漸近推斷的基礎知識。

作者簡介

Madhuri Kulkarni has been working as an Assistant Professor at the Department of Statistics, Savitribai Phule Pune University since 2003. She has taught a variety of courses in the span of 17 years. The list includes programming languages like C and C++, core statistical courses like probability distributions, statistical inference, regression analysis, and applied statistical courses like actuarial statistics, Bayesian inference, reliability theory. She has been using R for teaching the practical and applied courses for more than a decade. She is a recipient of the prestigious U. S. Nair Young Statistician Award. She has completed research projects for Armament Research and Development Establishment (ARDE), Pune, and has also received core research grant for a research project on software reliability from DST-SERB, India in 2018. She writes regularly in English, Hindi and Marathi in her blog. She also shares the e-content developed by her.

Shailaja Deshmukh is a visiting faculty at the Department of Statistics, Savitribai Phule Pune University (formerly known as University of Pune). She was earlier a Professor of Statistics and also Head of the Department of Statistics, before her retirement from the university in November 2015 after thirty eight years of service. She has taught around twenty five different theoretical and applied courses. She worked as a visiting professor at the Department of Statistics, University of Michigan, Ann Arbor, Michigan during 2009-10 academic year. Her areas of interest are inference in stochastic processes, applied probability, actuarial statistics and analysis of microarray data. She has a number of research publications in various peer-reviewed journals, such as Biometrika, Communication in Statistics (Theory and Methods), Journal of Multivariate Analysis, J. R. Statist. Soc. Australian Journal of Statistics, Biometrical Journal, Statistics and Probability Letters, Journal of Applied Statistics, Australian and New Zealand Journal of Statistics, Environmetrics, J. of Statistical Planning and Inference, Naval Research Logistics, Journal of Indian Statistical Association, Stochastic Modelling and Applications, Journal of Translational Medicine, Annals of Institute of Statistical Mathematics. She has published four books, the last of which was 'Multiple Decrement Models in Insurance: An Introduction Using R', published by Springer. She has served as an executive editor and as a chief editor of the Journal of Indian Statistical Association and is an elected member of the international Statistical Institute.

 

作者簡介(中文翻譯)

**Madhuri Kulkarni** 自 2003 年以來一直在薩維特里拜·普赫爾大學（Savitribai Phule Pune University）的統計系擔任助理教授。在這 17 年的時間裡，她教授了多種課程。這些課程包括 C 和 C++ 等程式語言、核心統計課程如機率分佈、統計推斷、迴歸分析，以及應用統計課程如精算統計、貝葉斯推斷、可靠性理論。她在教學實務和應用課程中使用 R 語言已超過十年。她是享有盛譽的美國奈爾年輕統計學家獎的獲得者。她為位於普納的武器研究與發展機構（Armament Research and Development Establishment, ARDE）完成了研究項目，並於 2018 年獲得印度 DST-SERB 的核心研究資助，用於一個有關軟體可靠性的研究項目。她定期在她的部落格中用英語、印地語和馬拉地語撰寫文章，並分享她所開發的電子內容。

**Shailaja Deshmukh** 是薩維特里拜·普赫爾大學（前稱普納大學）統計系的訪問教員。在 2015 年 11 月退休之前，她曾擔任統計學教授及統計系主任，並在該校服務了三十八年。她教授了約二十五門不同的理論和應用課程。在 2009-10 學年，她曾在密西根大學安娜堡分校的統計系擔任訪問教授。她的研究興趣包括隨機過程中的推斷、應用機率、精算統計和微陣列數據分析。她在多個同行評審的期刊上發表了多篇研究論文，如 *Biometrika*、*Communication in Statistics (Theory and Methods)*、*Journal of Multivariate Analysis*、*J. R. Statist. Soc.*、*Australian Journal of Statistics*、*Biometrical Journal*、*Statistics and Probability Letters*、*Journal of Applied Statistics*、*Australian and New Zealand Journal of Statistics*、*Environmetrics*、*J. of Statistical Planning and Inference*、*Naval Research Logistics*、*Journal of Indian Statistical Association*、*Stochastic Modelling and Applications*、*Journal of Translational Medicine*、*Annals of Institute of Statistical Mathematics*。她出版了四本書，最近一本是《保險中的多重減少模型：使用 R 的介紹》，由 Springer 出版。她曾擔任 *Journal of Indian Statistical Association* 的執行編輯和主編，並且是國際統計學會的當選成員。

類似商品