From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes (Frontiers in Probability and the Statistical Sciences) - Hardcover

Marie, Nicolas

Hardcover

ISBN 10: 3031956370 ISBN 13: 9783031956379

Verlag: Springer, 2025

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2025
• Sprache: Englisch
• ISBN 10: 3031956370
• ISBN 13: 9783031956379
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 196
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland