Smoothing of Multivariate Data: Density Estimation and Visualization / Edition 1 available in Hardcover
- Pub. Date:
An applied treatment of the key methods and state-of-the-art toolsfor visualizing and understanding statistical data
Smoothing of Multivariate Data provides an illustrative andhands-on approach to the multivariate aspects of densityestimation, emphasizing the use of visualization tools. Rather thanoutlining the theoretical concepts of classification andregression, this book focuses on the procedures for estimating amultivariate distribution via smoothing.
The author first provides an introduction to variousvisualization tools that can be used to construct representationsof multivariate functions, sets, data, and scales of multivariatedensity estimates. Next, readers are presented with an extensivereview of the basic mathematical tools that are needed toasymptotically analyze the behavior of multivariate densityestimators, with coverage of density classes, lower bounds,empirical processes, and manipulation of density estimates. Thebook concludes with an extensive toolbox of multivariate densityestimators, including anisotropic kernel estimators, minimizationestimators, multivariate adaptive histograms, and waveletestimators.
A completely interactive experience is encouraged, as allexamples and figurescan be easily replicated using the R softwarepackage, and every chapter concludes with numerous exercises thatallow readers to test their understanding of the presentedtechniques. The R software is freely available on the book'srelated Web site along with "Code" sections for each chapter thatprovide short instructions for working in the R environment.
Combining mathematical analysis with practical implementations,Smoothing of Multivariate Data is an excellent book for courses inmultivariate analysis, data analysis, and nonparametric statisticsat the upper-undergraduate and graduatelevels. It also serves as avaluable reference for practitioners and researchers in the fieldsof statistics, computer science, economics, and engineering.
About the Author
Jussi Klemel, 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.
Table of Contents
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.