Kernel SmoothingCRC Press, 1 груд. 1994 р. - 224 стор. Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function. This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilitated by the authors' focus on the simplest settings, namely density estimation and nonparametric regression. They pay particular attention to the problem of choosing the smoothing parameter of a kernel smoother, and also treat the multivariate case in detail. Kernal Smoothing is self-contained and assumes only a basic knowledge of statistics, calculus, and matrix algebra. It is an invaluable introduction to the main ideas of kernel estimation for students and researchers from other discipline and provides a comprehensive reference for those familiar with the topic. |
Зміст
Multivariate kernel density estimation | 4 |
Kernel regression | 114 |
Bandwidth selection | 139 |
Selected extra topics | 164 |
Appendices | 172 |
1 | 177 |
| 193 | |
| 208 | |
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Загальні терміни та фрази
AMISE analysis approximation asymptotic bandwidth h bandwidth matrix bandwidth selectors binwidth bivariate Chapter characteristic function choice computation cross-validation d-variate dashed curve denote density estimate based density f density function dependence derivatives direct plug-in distribution effective kernel Epanechnikov Figure function estimate given Hall and Marron hAMISE Härdle higher-order kernels histogram integrated squared bias Jones kernel density estimator kernel estimator kernel function kernel regression kernel smoothing kernel weights least squares linear kernel estimator local linear LSCV Marron mean squared error minimises MISE{ƒ Müller Nadaraya-Watson estimator nonparametric regression normal density normal mixture density notation obtain optimal bandwidth performance pilot bandwidth problem random variables rate of convergence regression estimators regression function Ruppert sample Scott second-order kernel Section selection Sheather shown shows solid curve standard normal kernel Statist symmetric Taylor's theorem theoretical univariate kernel variance vector Wand zero
Посилання на книгу
Monte Carlo Statistical Methods Christian Robert,George Casella Попередній перегляд недоступний - 2005 |