Jussi Klemelä 
Smoothing of Multivariate Data 
Density Estimation and Visualization

An 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 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, economics, and engineering.

Tabela de Conteúdo

Preface.

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.

Sobre o autor

Jussi KlemelÄ, Ph D, 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.