Maximum Penalized Likelihood Estimation: Vol.1 Maximum Penalized Likelihood Estimation
(Sprache: Englisch)
This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence...
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This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
Klappentext zu „Maximum Penalized Likelihood Estimation: Vol.1 Maximum Penalized Likelihood Estimation “
This book is intended for graduate students in statistics and industrial mathematics, as well as researchers and practitioners in the field. We cover 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. We also use (and develop from an elementary view point) discrete parameter submartingales and exponential inequalities. 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. Some theoretical topics that appear in textbook form for the first time are definitive treatments of I.J. Good's roughness penalization, monotone and unimodal density estimation, asymptotic optimality of generalized cross validation for spline smoothing and analogous methods for ill-posed least squares problems, and convergence proofs of EM algorithms for random sampling problems.
Inhaltsverzeichnis zu „Maximum Penalized Likelihood Estimation: Vol.1 Maximum Penalized Likelihood Estimation “
Parametric Maximum Likelihood Estimation Parametric Maximum Likelihood Estimation in Action Kernel Density Estimation Maximum Likelihood Density Estimation Monotone and Unimodal Densities Choosing the Smoothing Parameter Nonparametric Density Estimation in Action Convex Minimization in Finite Dimensional Spaces Convex Minimization in Infinite Dimensional Spaces Convexity in Action
Bibliographische Angaben
- Autor: Vincent N. LaRiccia
- 2001, 512 Seiten, 30 Abbildungen, Masse: 16,1 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387952683
- ISBN-13: 9780387952680
Sprache:
Englisch
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