Maximum Penalized Likelihood Estimation

Eggermont, Paul P.; LaRiccia, Vincent N.

ISBN 10: 1461417120 / ISBN 13: 9781461417125

Published by Springer-Verlag New York Inc., 2011

About this Item

Ideal for researchers and practitioners in statistics and industrial mathematics, this book covers the theory and practice of nonparametric estimation. It is novel in its use of maximum penalized likelihood estimation and convex minimization problem theory. Series: Springer Series in Statistics. Num Pages: 592 pages, biography. BIC Classification: PBC; TJF; UYQV. Category: (G) General (US: Trade). Dimension: 235 x 155 x 30. Weight in Grams: 896. . 2011. Paperback. . . . .

Seller Inventory # V9781461417125

Bibliographic Details

• Title: Maximum Penalized Likelihood Estimation
• Publisher: Springer-Verlag New York Inc.
• Publication Date: 2011
• Language: English
• ISBN 10: 1461417120
• ISBN 13: 9781461417125
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This book is intended for graduate students in statistics and industrial mathematics, as well as researchers and practitioners in the field. It covers both theory and practice of nonparametric estimation. The text is novel in its use of maximum penalized likelihood estimation, and the theory of convex minimization problems (fully developed in the text) to obtain convergence rates. A substantial effort has been made to discuss computational details, and to include simulation studies and analyses of some classical data sets using fully automatic (data driven) procedures.

From the Back Cover

This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in statistics, operations research and applied mathematics, as well as for researchers and practitioners in the field. The present volume deals with nonparametric regression.

The emphasis in this volume is on smoothing splines of arbitrary order, but other estimators (kernels, local and global polynomials) pass review as well. Smoothing splines and local polynomials are studied in the context of reproducing kernel Hilbert spaces. The connection between smoothing splines and reproducing kernels is of course well-known. The new twist is that letting the innerproduct depend on the smoothing parameter opens up new possibilities. It leads to asymptotically equivalent reproducing kernel estimators (without qualifications), and thence, via uniform error bounds for kernel estimators, to uniform error bounds for smoothing splines and via strong approximations, to confidence bands for the unknown regression function.

The reason for studying smoothing splines of arbitrary order is that one wants to use them for data analysis. Regarding the actual computation, the usual scheme based on spline interpolation is useful for cubic smoothing splines only. For splines of arbitrary order, the Kalman filter is the most important method, the intricacies of which are explained in full. The authors also discuss simulation results for smoothing splines and local and global polynomials for a variety of test problems as well as results on confidence bands for the unknown regression function based on undersmoothed quintic smoothing splines with remarkably good coverage probabilities.

P.P.B. Eggermont and V.N. LaRiccia are with the Statistics Program of the Department of Food and Resource Economics in the College of Agriculture and Natural Resources at the University of Delaware, and the authors of Maximum Penalized Likelihood Estimation: Volume I: Density Estimation.