Multivariate Density Estimation: Theory, Practice, and VisualizationDensity estimation has long been recognized as an important tool when used with univariate and bivariate data. But the computer revolution of recent years has provided access to data of unprecedented complexity in ever-growing volume. New tools are required to detect and summarize the multivariate structure of these difficult data. Multivariate Density Estimation: Theory, Practice, and Visualization demonstrates that density estimation retains its explicative power even when applied to trivariate and quadrivariate data. By presenting the major ideas in the context of the classical histogram, the text simplifies the understanding of advanced estimators and develops links between the intuitive histogram and other methods that are more statistically efficient. The theoretical results covered are those particularly relevant to application and understanding. The focus is on methodology, new ideas, and practical advice. A hierarchical approach draws attention to the similarities among different estimators. Also, detailed discussions of nonparametric dimension reduction, nonparametric regression, additive modeling, and classification are included. Because visualization is a key element in effective multivariate nonparametric analysis, more than 100 graphic illustrations supplement the numerous problems and examples presented in the text. In addition, sixteen four-color plates help to convey an intuitive feel for both the theory and practice of density estimation in several dimensions. Ideal as an introductory textbook, Multivariate Density Estimation is also an indispensable professional reference for statisticians, biostatisticians, electrical engineers, econometricians, and other scientistsinvolved in data analysis. |
Contents
Nonparametric Estimation Criteria | 33 |
Theory and Practice | 47 |
Averaged Shifted Histograms | 113 |
Kernel Density Estimators | 125 |
33 | 145 |
The Curse of Dimensionality and Dimension | 195 |
Nonparametric Regression and Additive Models | 219 |
Appendix A Computer Graphics in R³ | 267 |
Appendix B Data Sets | 273 |
Notation | 281 |
Other editions - View all
Multivariate Density Estimation: Theory, Practice, and Visualization David W. Scott Limited preview - 2009 |
Multivariate Density Estimation: Theory, Practice, and Visualization David W. Scott No preview available - 2009 |
Common terms and phrases
algorithm AMISE applied approximation ASH estimates asymptotic averaged shifted histogram bandwidth BCV(h bivariate biweight kernel bootstrap boundary kernels bumps Chernoff faces choice clusters computed Consider criterion cross-validation curse of dimensionality curve data points data set density function derivative dimensions displayed Epanechnikov equal Equation equivalent kernel example factor finite frequency polygon graphical higher-order kernels interval kernel density estimator kernel estimate kernel regression matrix minimizer mixture density multivariate naive ASH nbin nonparametric estimators nonparametric regression Normal data Normal density Normal kernel number of bins optimal bin width oversmoothed bandwidth parallel coordinates parametric estimator plot pointwise polynomial problem product kernel projection pursuit random variable ratio regression result roughness sample sizes scatter diagrams scatterplot Scott Section shown in Figure skewness smoother smoothing parameter snowfall inches solution spline squared bias Statistical Table Terrell Theorem transformation triangle trivariate Tukey univariate values variance vector visualization weights
Popular passages
Page 292 - MARSHALL, AW and OLKIN, I. (1985). A family of bivariate distributions generated by the bivariate Bernoulli distribution, J.
Page 292 - Toward a practical method which helps uncover the structure of a set of multivariate observations by finding the linear transformation which optimizes a new 'index of condensation,' " in Statistical Computation, RC Milton and JA Nelder, Ed.