An Introduction to Copulas
An Introduction to Copulas
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DOI：
10.1080/00401706.2000.10486066
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发表时间：
2000-08
期刊：
影响因子：
2.5
通讯作者：
Bill Ravens
中科院分区：
文献类型：
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作者：
Bill Ravens
第7章深入讨论了密度估计量、阈值、非线性密度估计量、多元小波估计量和多尺度估计量的使用。第八章概述了贝叶斯推断，它利用数据和先验信息来选择一种不那么特别的收缩过程来进行密度估计。第九章对小波变换的应用及其应用于随机时间序列的性质进行了综述。事实上，这一章的大部分内容都是关于小波在估计谱密度中的应用，然后它简要地提到了小波谱的性质。最有意义的是小波变换的白化性质，因为它们是平稳随机时间序列的近似特征函数。对于应用从业者来说，这是一个重要的属性。我希望作者在这一部分有更多的阐述，并说明小波变换与主成分分析的相似之处。还缺乏使用该属性进行在线建模和监控的实例。第10章-L第1章描述了如何使用小波来产生随机密度，并参考了小波的其他各种统计应用，如湍流。这本书不适合技术计量学的普通读者，因为它是一本关于小波的入门教科书。正如作者所指出的，“这本书的目标读者是统计学或数学专业的研究生，以及实习统计学家”，“需要精通高等微积分”。对于满足这些要求的读者，或者那些刚刚熟悉小波理论、数学倾向并想了解更多内容的读者，这本书将是一本有趣的书。它写得很好，组织得很好，有紧凑的派生和广泛的参考资料，可以作为关于小波这个令人兴奋的主题的非常好的参考资料。
Chapter 7 covers, in depth, density estimators, thresholding, the use of nonlinear density estimators, multivariate wavelets estimators, and multiscale estimators. Chapter 8 provides an overview of Bayesian inference, which makes use of the data and prior information to select a less ad hoc shrinkage procedure for density estimation. Chapter 9 attempts to give an overview of the use of wavelet transform and its properties as applied to stochastic time series. In fact most of the chapter deals with the use of wavelets in estimating spectral densities, and then it briefly mentions the properties of the wavelets spectrum. Of pititular interest are the whitening properties of wavelet transform because they are approximate eigenfunctions to stationary stochastic time series. This is an important property for applied practitioners. I wish the author had expanded on this section and showed the similarity of wavelet transform to principal components analysis. Examples illustrating the use of this property for online modeling and monitoring are also lacking. Chapters 10-l 1 describe the use of wavelets to generate random densities and have references to miscellaneous other statistical applications of wavelets such as turbulence. This is not a book for casual readers of Technometrics as an introductory textbook on wavelets. As the author points out, “This book is aimed at graduate students in statistics or mathematics, and practicing statisticians” and “requires proficiency in advanced calculus.” For readers meeting these requirements, or those just familiar with wavelet theory, mathematically inclined, and wanting to learn more, the book will be enjoyable and interesting. It is well written and organized with compact derivations and extensive references and can serve as a very good reference on the exciting topic of wavelets.