# Seminar on Stochastic Analysis, Random Fields and Applications VIStatistical Inference and Malliavin Calculus

Seminar on Stochastic Analysis, Random Fields and Applications VI: Statistical Inference and... [The derivative of the log-likelihood function, known as score function, plays a central role in parametric statistical inference. It can be used to study the asymptotic behavior of likelihood and pseudo-likelihood estimators. For instance, one can deduce the local asymptotic normality property which leads to various asymptotic properties of these estimators. In this article we apply Malliavin Calculus to obtain the score function as a conditional expectation. We then show, through different examples, how this idea can be useful for asymptotic inference of stochastic processes. In particular, we consider situations where there are jumps driving the data process.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Seminar on Stochastic Analysis, Random Fields and Applications VIStatistical Inference and Malliavin Calculus

Part of the Progress in Probability Book Series (volume 63)
Editors: Dalang, Robert; Dozzi, Marco; Russo, Francesco
24 pages

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# References (35)

Publisher
Springer Basel
ISBN
978-3-0348-0020-4
Pages
59 –82
DOI
10.1007/978-3-0348-0021-1_4
Publisher site
See Chapter on Publisher Site

### Abstract

[The derivative of the log-likelihood function, known as score function, plays a central role in parametric statistical inference. It can be used to study the asymptotic behavior of likelihood and pseudo-likelihood estimators. For instance, one can deduce the local asymptotic normality property which leads to various asymptotic properties of these estimators. In this article we apply Malliavin Calculus to obtain the score function as a conditional expectation. We then show, through different examples, how this idea can be useful for asymptotic inference of stochastic processes. In particular, we consider situations where there are jumps driving the data process.]

Published: Feb 4, 2011

Keywords: Diffusion processes; Malliavin calculus; parametric estimation; Cramer-Rao lower bound; LAN property; LAMN property; jump-diffusion processes; score function