Exponential families of stochastic processes
type: Item
instance of: scholarly article
title: Exponential families of stochastic processes
zbMATH Open document ID: 0882.60012
author: Uwe Küchler
author: Michael Sørensen
published in: Springer Series in Statistics
publication date: 1997-08-19T00:00:00Z
review text: Exponential models play a central role in classical statistical theory. There are at least three reasons for studying the classical exponential families of probability distributions. They are analytically tractable models, they have several nice statistical properties, and a large part of the models used in statistical practice are exponential families. The authors study what role exponential families play in statistical inference for stochastic processes. The book contains 12 chapters and an appendix. A considerable portion of this one is focused on likelihood theory for general exponential families of stochastic processes. The other main themes are asymptotic likelihood theory and sequential maximum likelihood estimation. This book will assist graduate students as well as researchers in statistics not only in getting into the problems of inference for stochastic processes by studying the most tractable type of models, but also in learning to solve the problems by the tools of stochastic calculus. Most of the concepts from stochastic calculus are introduced and explained without proof in an appendix.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 62-02
zbMATH DE Number: 1049649
zbMATH Keywords: exponential models
zbMATH Keywords: statistical inference for stochastic processes
zbMATH Keywords: likelihood theory for general exponential families
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: b98954
OpenAlex ID: W1977400475
DOI: 10.1007/B98954
description: scientific article; zbMATH DE number 1049649