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

著者名：Marie, Nicolas

Springer（2025/09/26発売）

• 言語：ENG
• ISBN：9783031956379
• eISBN：9783031956386

Description

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.

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.