Description
Book SynopsisAn applied treatment of the key methods and state-of-the-art tools for visualizing and understanding statistical data
Smoothing 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 extensiv
Trade Review
"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)
Table of ContentsPreface.
Introduction.
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.
