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Theory of Spatial Statistics: A Concise Introduction
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2020-04-02 , DOI: 10.1080/01621459.2020.1759991
Frederic P. Schoenberg 1
Affiliation  

Chapter 1 introduces many of the mathematical concepts required to understand the remainder of the book before previewing the key ideas of the linear conditional mean assumption and the central subspace discussed in Chapter 2. Chapters 3–6 describe techniques for estimating the central subspace. Specifically, Chapters 3 and 4 focus on first-order methods such as sliced inverse regression and the related parametric and kernel inverse regression methods while Chapters 5 and 6 introduce second-order methods with the additional assumption of constant conditional variance. Chapters 7–10 undertake a diversion from the development of methodology. Chapter 7 investigates the key assumptions from the previous chapters and their relation with elliptically contoured distributions. Chapter 8 simplifies the task to the estimation of the central mean subspace, replacing the SDR conditional independence assumption (that Y ⊥⊥ X | X for some matrix ) with an assumption on the conditional mean:

中文翻译:

空间统计理论:简明介绍

在预览第 2 章中讨论的线性条件均值假设和中心子空间的关键思想之前,第 1 章介绍了理解本书其余部分所需的许多数学概念。第 3-6 章描述了估计中心子空间的技术。具体来说,第 3 章和第 4 章侧重于一阶方法,例如切片逆回归以及相关的参数和核逆回归方法,而第 5 章和第 6 章则介绍了附加条件方差恒定假设的二阶方法。第 7 章到第 10 章从方法论的发展中转移了注意力。第 7 章研究了前几章的关键假设及其与椭圆轮廓分布的关系。第 8 章将任务简化为中心平均子空间的估计,
更新日期:2020-04-02
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