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portada From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
Type
Physical Book
Publisher
Author
Language
English
Pages
184
Format
Hardcover
Dimensions
23.7 x 16.5 x 1.7 cm
ISBN13
9783031956379

From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes

Marie, Nicolas (Author) · Springer · Hardcover

From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes - Marie, Nicolas

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Synopsis "From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes"

This book is about copies-based nonparametric estimation of the drift function in stochastic differential equations (SDEs) driven by Brownian motion, a jump process, or fractional Brownian motion. While the estimators of the drift function in SDEs are classically computed from one long-time observation of the ergodic stationary solution, here the estimation framework - which is part of functional data analysis - involves multiple copies of the (non-stationary) solution observed over a short-time interval. Two kinds of nonparametric estimators are investigated for SDE models, first presented in the regression framework: the projection least squares estimator and the Nadaraya-Watson estimator. Adaptive procedures are provided for possible applications in statistical learning. Primarily intended for researchers in statistical inference for stochastic processes who are interested in the copies-based observation scheme, the book will also be useful for graduate and PhD students in probability and statistics, thanks to its multiple reminders of the requisite theory, especially the chapter on nonparametric regression.

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