M-statistics: Optimal Statistical Inference for a Small Sample 1st Edition
暫譯: M-統計量:小樣本的最佳統計推斷 第1版

Demidenko, Eugene

  • 出版商: Wiley
  • 出版日期: 2023-08-22
  • 售價: $4,410
  • 貴賓價: 9.5$4,190
  • 語言: 英文
  • 頁數: 240
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1119891795
  • ISBN-13: 9781119891796
  • 相關分類: 機率統計學 Probability-and-statistics
  • 海外代購書籍(需單獨結帳)

商品描述

A comprehensive resource providing new statistical methodologies and demonstrating how new approaches work for applications

M-statistics introduces a new approach to statistical inference, redesigning the fundamentals of statistics and improving on the classical methods we already use. This book targets exact optimal statistical inference for a small sample under one methodological umbrella. Two competing approaches are offered: maximum concentration (MC) and mode (MO) statistics combined under one methodological umbrella, which is why the symbolic equation M=MC+MO. M-statistics defines an estimator as the limit point of the MC or MO exact optimal confidence interval when the confidence level approaches zero, the MC and MO estimator, respectively. Neither mean nor variance plays a role in M-statistics theory.

Novel statistical methodologies in the form of double-sided unbiased and short confidence intervals and tests apply to major statistical parameters:

  • Exact statistical inference for small sample sizes is illustrated with effect size and coefficient of variation, the rate parameter of the Pareto distribution, two-sample statistical inference for normal variance, and the rate of exponential distributions.
  • M-statistics is illustrated with discrete, binomial and Poisson distributions. Novel estimators eliminate paradoxes with the classic unbiased estimators when the outcome is zero.
  • Exact optimal statistical inference applies to correlation analysis including Pearson correlation, squared correlation coefficient, and coefficient of determination. New MC and MO estimators along with optimal statistical tests, accompanied by respective power functions, are developed.
  • M-statistics is extended to the multidimensional parameter and illustrated with the simultaneous statistical inference for the mean and standard deviation, shape parameters of the beta distribution, the two-sample binomial distribution, and finally, nonlinear regression.

Our new developments are accompanied by respective algorithms and R codes, available at GitHub, and as such readily available for applications.

M-statistics is suitable for professionals and students alike. It is highly useful for theoretical statisticians and teachers, researchers, and data science analysts as an alternative to classical and approximate statistical inference.

商品描述(中文翻譯)

提供新統計方法的綜合資源,並展示新方法如何應用於實際情境

M-statistics 介紹了一種新的統計推斷方法,重新設計統計學的基本原則,並改進我們已經使用的經典方法。本書針對在一個方法論框架下的小樣本的精確最佳統計推斷。提供了兩種競爭的方法:最大集中度 (MC) 和模式 (MO) 統計,這就是為什麼有符號方程式 M=MC+MO。M-statistics 將估計量定義為當信賴水平接近零時,MC 或 MO 精確最佳信賴區間的極限點,分別為 MC 和 MO 估計量。在 M-statistics 理論中,均值和方差並不扮演角色。

新穎的統計方法以雙側無偏和短信賴區間及檢定的形式應用於主要統計參數:


  • 小樣本的精確統計推斷以效應大小和變異係數、帕累托分佈的速率參數、正態變異的兩樣本統計推斷以及指數分佈的速率進行說明。

  • M-statistics 以離散、二項和泊松分佈進行說明。新穎的估計量消除了當結果為零時經典無偏估計量的悖論。

  • 精確最佳統計推斷適用於相關分析,包括 Pearson 相關、平方相關係數和決定係數。新開發的 MC 和 MO 估計量以及最佳統計檢定,伴隨相應的檢定力函數。

  • M-statistics 擴展到多維參數,並以均值和標準差的同時統計推斷、貝塔分佈的形狀參數、兩樣本二項分佈,最後是非線性回歸進行說明。

我們的新發展伴隨相應的算法和 R 代碼,並可在 GitHub 上獲得,因此可隨時應用。

M-statistics 適合專業人士和學生使用。對於理論統計學家和教師、研究人員以及數據科學分析師來說,作為經典和近似統計推斷的替代方案,具有很高的實用性。

作者簡介

Eugene Demidenko is Professor of Biomedical Data Science at the Geisel School of Medicine and Mathematics at Dartmouth. He is a member of the American Statistical Association (ASA) and the Society of Industrial and Applied Mathematics (SIAM). In statistics, Professor Demidenko's research includes statistical methodology, mixed models, and nonlinear regression. In applied mathematics, he contributed to existence and uniqueness of global minimum, tumor regrowth theory, shape and image analysis, and solving ill-posed problems via mixed boundary partial differential equations. He is the author of two books published by Wiley in 2013 and 2020 "Mixed Models: Theory and Applications" and "Advanced Statistics with Applications in R." The latter book received a prestigious Ziegel Book Award in Statistics from Technometrics/ASA journal in 2022.

作者簡介(中文翻譯)

尤金·德米登科是達特茅斯醫學與數學學院的生物醫學數據科學教授。他是美國統計協會(ASA)和工業與應用數學學會(SIAM)的成員。在統計學方面,德米登科教授的研究包括統計方法學、混合模型和非線性回歸。在應用數學方面,他對全局最小值的存在性和唯一性、腫瘤再生理論、形狀與影像分析,以及通過混合邊界偏微分方程解決病態問題做出了貢獻。他是2013年和2020年由Wiley出版的兩本書的作者,分別是《混合模型:理論與應用》和《R的進階統計應用》。後者在2022年獲得了Technometrics/ASA期刊頒發的著名Ziegel統計書獎。