Trimmed likelihood estimators for stochastic differential equations with an application to crack growth analysis from photos
Loading...
Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We introduce trimmed likelihood estimators for processes given by a
stochastic differential equation for which a transition density is known or can
be approximated and present an algorithm to calculate them. To measure the
fit of the observations to a given stochastic process, two performance measures
based on the trimmed likelihood estimator are proposed. The approach is applied
to crack growth data which are obtained from a series of photos by backtracking
large cracks which were detected in the last photo. Such crack growth
data are contaminated by several outliers caused by errors in the automatic
image analysis. We show that trimming 20% of the data of a growth curve
leads to good results when 100 obtained crack growth curves are fitted with
the Ornstein-Uhlenbeck process and the Cox-Ingersoll-Ross processes while
the fit of the Geometric Brownian Motion is significantly worse. The method
is sensitive in the sense that crack curves obtained under different stress conditions
provide significantly different parameter estimates.