Smoothing of Multivariate Data
Density Estimation and Visualization
(Sprache: Englisch)
This comprehensive resource provides the algorithmic methods and state of the art tools to successfully visualize statistical data. The coverage offers insight into underlying processes of density estimation, emphasizing use of visualization tools rather...
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This comprehensive resource provides the algorithmic methods and state of the art tools to successfully visualize statistical data. The coverage offers insight into underlying processes of density estimation, emphasizing use of visualization tools rather than only the theoretical concepts of classification and regression.
Klappentext zu „Smoothing of Multivariate Data “
An applied treatment of the key methods and state-of-the-art tools for visualizing and understanding statistical dataSmoothing of Multivariate Data provides an illustrative and hands-on approach to the multivariate aspects of density estimation, emphasizing the use of visualization tools. Rather than outlining the theoretical concepts of classification and regression, this book focuses on the procedures for estimating a multivariate distribution via smoothing.
The author first provides an introduction to various visualization tools that can be used to construct representations of multivariate functions, sets, data, and scales of multivariate density estimates. Next, readers are presented with an extensive review of the basic mathematical tools that are needed to asymptotically analyze the behavior of multivariate density estimators, with coverage of density classes, lower bounds, empirical processes, and manipulation of density estimates. The book concludes with an extensive toolbox of multivariate density estimators, including anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, and wavelet estimators.
A completely interactive experience is encouraged, as all examples and figurescan be easily replicated using the R software package, and every chapter concludes with numerous exercises that allow readers to test their understanding of the presented techniques. The R software is freely available on the book's related Web site along with "Code" sections for each chapter that provide short instructions for working in the R environment.
Combining mathematical analysis with practical implementations, Smoothing of Multivariate Data is an excellent book for courses in multivariate analysis, data analysis, and nonparametric statistics at the upper-undergraduate and graduatelevels. It also serves as a valuable reference for practitioners and researchers in the fields of statistics, computer science,
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economics, and engineering.
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This comprehensive resource provides the algorithmic methods and state-of-the-art tools to successfully visualize statistical data. The coverage offers insight into underlying processes of density estimation, emphasizing use of visualization tools rather than only the theoretical concepts of classification and regression. The book is highly interactive in nature, as all figures and experiments can be reproduced via the two R software packages used throughout and available on a related Web site. Over 200 illustrations depict the discussed visualizations and "Examples" sections, making this both an dynamic text for students and a working reference for professionals.
Inhaltsverzeichnis zu „Smoothing of Multivariate Data “
PrefaceIntroduction
PART I VISUALIZATION
1. Visualization of Data
2. Visualization of Functions
3. Visualization of Trees
4. Level Set Trees
5. Shape Trees
6. Tail Trees
7. Scales of Density Estimates
8. Cluster Analysis
PART II ANALYTICAL AND ALGORITHMIC TOOLS
9. Density Estimation
10. Density Classes
11. Lower Bounds
12. Empirical Processes
13. Manipulation of Density Estimates
PART III TOOLBOX OF DENSITY ESTIMATORS
14. Local Averaging
15. Minimization Eestimators
16 Wavelet Estimators
17. Multivariate Adaptive Hhistograms
18. Best Basis Selection
19. Stagewise Minimization
Appendix A: Notations
Appendix B: Formulas
Appendix C: The parentchild relations in a modegraph
Appendix D: Trees
Appendix E: Proofs
Problem Solving
References
Author Index
Topic Index
Autoren-Porträt von Jussi Klemelä
Jussi KlemelÄ, PhD, is Researcher in the Department of Mathematical Sciences at the University of Oulu, Finland. Dr. Klemelä has authored or coauthored numerous journal articles on his areas of research interest, which include density estimation and the implementation of cutting edge visualization tools.
Bibliographische Angaben
- Autor: Jussi Klemelä
- 2009, 1. Auflage, 640 Seiten, Maße: 23,8 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470290889
- ISBN-13: 9780470290880
- Erscheinungsdatum: 18.09.2009
Sprache:
Englisch
Pressezitat
"Overall, the book complements existing books on nonparametric density estimation with its focus on multivariate data, visualization and sieve type estimators." (Mathematical Reviews, 2011) "The book is suitable for courses in data analysis, multivariate analysis, and nonparametric statistics at the upper undergraduate and graduate levels. Since it combines mathematical analysis with practical implementation it is also recommended to practitioners and researchers in the fields of statistics, computer science, economics and engineering." (Zentralblatt MATH, 2011)
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