From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
This book is about copies-based nonparametric estimation of the drift function in shastic 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 shastic 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.

1147389498
From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
This book is about copies-based nonparametric estimation of the drift function in shastic 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 shastic 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.

129.99 Out Of Stock
From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes

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

by Nicolas Marie
From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes
Add to Wishlist
From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes

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

by Nicolas Marie

Overview

This book is about copies-based nonparametric estimation of the drift function in shastic 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 shastic 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.

Product Details

ISBN-13: 9783031956379
Publisher: Springer Nature Switzerland
Publication date: 09/27/2025
Series: Frontiers in Probability and the Statistical Sciences
Pages: 184
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

Nicolas Marie is an associate professor in the Modal’X department at Paris Nanterre University. He received his PhD in probability in 2012, and his habilitation in statistics and probability in 2019. First, in the rough paths theory framework, he focused on constrained fractional diffusions. Then, since 2017, Nicolas Marie contributes to investigate the copies-based statistical inference for diffusions and fractional diffusions.

Table of Contents

Introduction.- Nonparametric regression: a detailed reminder.- The projection least squares estimator of the drift function.- Going further with the projection least squares method: diffusions with jumps and fractional diffusions.- The Nadaraya-Watson estimator of the drift function.

From the B&N Reads Blog
Page 1 of

Related Subjects

Science & Technology
Mathematics
Probability Theory
Statistics
Science & Technology
Mathematics
Probability Theory
Statistics

Customer Reviews