Jussi Klemelä

Smoothing of Multivariate Data (eBook, PDF)

Density Estimation and Visualization

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 648
• Erscheinungstermin: 07.09.2009
• Englisch
• ISBN-13: 9780470425664
• Artikelnr.: 37292079

Autorenporträt

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.

Inhaltsangabe

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