"I am very impressed with this book. It addresses issues that are not discussed in any detail in any other book on density estimation. Furthermore, it is very well-written and contains a wealth of interesting examples. In fact, this is probably one of the best books I have seen on density estimation. Some topics in this book that are not covered in detail in any other book include: multivariate bandwidth matrices, details of the asymptotic MSE for general bandwidth matrices, derivative estimation, level sets, density clustering and significance testing for modal regions. This makes the book unique. The authors have written the book in such a way that it can be used by two different types of readers: data analysts who are not interested in the mathematical details, and students/researchers who do want the details. The `how to read this monograph' is very useful."
~Larry Wasserman, Carnegie Mellon University
"This book provides a comprehensive overview of the fundamental issues and the numerous extensions of multivariate kernel density estimation. There are three core aspects that are discussed. Firstly, the method of kernel density estimation is thoroughly described in the multivariate setting. Secondly, the problem of selecting a bandwidth matrix is discussed, with a comparison of numerous alternatives. Thirdly, the performance and asymptotic properties of the estimators and bandwidth selections are comprehensively reviewed: there is an abundance of information on the (asymptotic) mean (integrated) squared error of various combinations of estimators and bandwidths.
Having examined the above fundamentals, the authors discuss numerous extensions of multivariate kernel density estimation. These include density derivative estimation, level set estimation, density-based clustering, density ridge estimation, feature significance, density di erence estimation, and classification. For all of these methods, there is a strong focus on asymptotic performance. There are also advice on and examples of providing e ective visual communication of results. Guidance on the application of the methods is limited to descriptions of the R commands available in the fs package.
The structure of the book means that all the above methods have accessible explanations, while detailed and thorough mathematical exposition is maintained. Each chapter or section is structured such that the methods are first described and then illustrated, and then the technical mathematical details (including proofs of theorems) are supplied. This brings about the authors' stated aim of the book being useful for data analysts, undergraduates or postgraduates."
~Andrew Duncan A. C. Smith
"Overall, it was a great joy for me to review this book. It was written beautifully. The authors offered many valuable insights on multivariate kernel smoothing, which I found helpful. I am looking forward to having a copy onmy bookshelf and I have no doubt that it will be my research reference book in the future."
~QingWang, Wellesley College
"I am very impressed with this book. It addresses issues that are not discussed in any detail in any other book on density estimation. Furthermore, it is very well-written and contains a wealth of interesting examples. In fact, this is probably one of the best books I have seen on density estimation. Some topics in this book that are not covered in detail in any other book include: multivariate bandwidth matrices, details of the asymptotic MSE for general bandwidth matrices, derivative estimation, level sets, density clustering and significance testing for modal regions. This makes the book unique. The authors have written the book in such a way that it can be used by two different types of readers: data analysts who are not interested in the mathematical details, and students/researchers who do want the details. The `how to read this monograph' is very useful."
~Larry Wasserman, Carnegie Mellon University
"This book provides a comprehensive overview of the fundamental issues and the numerous extensions of multivariate kernel density estimation. There are three core aspects that are discussed. Firstly, the method of kernel density estimation is thoroughly described in the multivariate setting. Secondly, the problem of selecting a bandwidth matrix is discussed, with a comparison of numerous alternatives. Thirdly, the performance and asymptotic properties of the estimators and bandwidth selections are comprehensively reviewed: there is an abundance of information on the (asymptotic) mean (integrated) squared error of various combinations of estimators and bandwidths.
Having examined the above fundamentals, the authors discuss numerous extensions of multivariate kernel density estimation. These include density derivative estimation, level set estimation, density-based clustering, density ridge estimation, feature significance, density di erence estimation, and classification. For all of these methods, there is a strong focus on asymptotic performance. There are also advice on and examples of providing e ective visual communication of results. Guidance on the application of the methods is limited to descriptions of the R commands available in the fs package.
The structure of the book means that all the above methods have accessible explanations, while detailed and thorough mathematical exposition is maintained. Each chapter or section is structured such that the methods are first described and then illustrated, and then the technical mathematical details (including proofs of theorems) are supplied. This brings about the authors' stated aim of the book being useful for data analysts, undergraduates or postgraduates."
~Andrew Duncan A. C. Smith
"Overall, it was a great joy for me to review this book. It was written beautifully. The authors offered many valuable insights on multivariate kernel smoothing, which I found helpful. I am looking forward to having a copy onmy bookshelf and I have no doubt that it will be my research reference book in the future."
~QingWang, Wellesley College
