Functional Estimation for Density, Regression Models and Processes

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World Scientific, 2011 - Mathematics - 199 pages
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This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators.It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators.
 

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Contents

1 Introduction
1
2 Kernel estimator of a density
23
3 Kernel estimator of a regression function
49
4 Limits for the varying bandwidths estimators
75
5 Nonparametric estimation of quantiles
87
6 Nonparametric estimation of intensities for stochastic processes
107
7 Estimation in semiparametric regression models
137
8 Diffusion processes
147
9 Applications to time series
167
10 Appendix
183
Notations
189
Bibliography
191
Index
197
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