Multivariate Density Estimation : Theory, Practice, and Visualization

David W. Scott
Bok · Engelsk · 2009 · Electronic books.

Annen tittel	Wiley Series in Probability and Statistics
Utgitt	Hoboken : : Wiley, , 2009.
Omfang	1 online resource (350 p.)
Opplysninger	Description based upon print version of record.. - Multivariate Density Estimation Theory, Practice, and Visualization; Contents; Preface; 1. Representation and Geometry of Multivariate Data; 1.1. Introduction; 1.2. Historical Perspective; 1.3. Graphical Display of Multivariate Data Points; 1.4. Graphical Display of Multivariate Functionals; 1.5. Geometry of Higher Dimensions; Problems; 2. Nonparametric Estimation Criteria; 2.1. Estimation of the Cumulative Distribution Function; 2.2. Direct Nonparametric Estimation of the Density; 2.3. Error Criteria for Density Estimates; 2.4. Nonparametric Families of Distributions; Problems. - 3. Histograms: Theory and Practice3.1. Sturges' Rule for Histogram Bin Width Selection; 3.2. The L2 Theory of Univariate Histograms; 3.3. Practical Data-Based Bin Width Rules; 3.4. L2 Theory for Multivariate Histograms; 3.5. Modes and Bumps in a Histogram; 3.6. Other Error Criteria: L1, L4, L6, L8, and Lx; Problems; 4. Frequency PoIygons; 4.1. Univariate Frequency Polygons; 4.2. Multivariate Frequency Polygons; 4.3. Bin Edge Problems; Problems; 5. Averaged Shifted Histograms; 5.1. Construction; 5.2. Asymptotic Properties; 5.3. The Limiting ASH as a Kernel Estimator; Problems. - 6. Kernel Density Estimators6.1. Motivation for Kernel Estimators; 6.2. Theoretical Properties: Univariate Case; 6.3. Theoretical Properties: Multivariate Case; 6.4. Generality of the Kernel Method; 6.5. Cross-Validation; 6.6. Adaptive Smoothing; Problems; 7. The Curse of DimensionaIity and Dimension Reduction; 7.1. Introduction; 7.2. Curse of Dimensionality; 7.3. Dimension Reduction; Problems; 8. Nonparametric Regression and Additive Models; 8.1. Nonparametric Kernel Regression; 8.2. General Linear Nonparametric Estimation; 8.3. Robustness; 8.4. Regression in Several Dimensions; 8.5. Summary. - Problems9. Other Applications; 9.1. Classification, Discrimination, and Likelihood Ratios; 9.2. Modes and Bump Hunting; 9.3. Specialized Topics; Problems; Appendix A. Computer Graphics in R3; A.1. Bivariate and Trivariate Contouring Display; A.2. Drawing 3-D Objects on the Computer; Appendix B. Data Sets; B.1. United States Economic Variables Data; B.2. University Data; B.3. Blood Fat Concentration Data; B.4. Penny Thickness Data; B.5. Gas Meter Accuracy Data; B.6. Old Faithful Data; B.7. Silica Data; 8.8. LRL Data; B.9 Buffalo Snowfall Data; Appendix C. Notation; References; Author Index. - Subject Index. - Written to convey an intuitive feel for both theory and practice, its main objective is to illustrate what a powerful tool density estimation can be when used not only with univariate and bivariate data but also in the higher dimensions of trivariate and quadrivariate information. Major concepts are presented in the context of a histogram in order to simplify the treatment of advanced estimators. Features 12 four-color plates, numerous graphic illustrations as well as a multitude of problems and solutions.
Emner	Estimation theory Multivariate analysis Mathematical Statistics Mathematics Vis mer... Physical Sciences & Mathematics multivariabel analyse
Sjanger	Electronic books.
Dewey	519
ISBN	0471547700