2008, English, Article edition: Parameter estimation for a bidimensional partially observed Ornstein-Uhlenbeck process with biological application Favetto, Benjamin; Samson, Adeline

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Bookmark: http://trove.nla.gov.au/version/200660
Physical Description
  • text
Published
  • HAL - CCSD
  • 2008
Language
  • English

Edition details

Title
  • Parameter estimation for a bidimensional partially observed Ornstein-Uhlenbeck process with biological application
Author
  • Favetto, Benjamin
  • Samson, Adeline
Published
  • HAL - CCSD
  • 2008
Physical Description
  • text
Subjects
Notes
  • We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalman filter recursion. We also propose a recursive computation of the gradient and hessian of the log-likelihood based on Kalman filtering, which allows to implement an easy numerical maximisation of the likelihood and the exact maximum likelihood estimator (MLE). Furthermore, we establish the link between the observations and an ARMA process and we deduce the asymptotic properties of the MLE. We show that this ARMA property can be generalised to a higher dimensional underlying Ornstein-Uhlenbeck diffusion. We compare this estimator with the one obtained by the well-known EM algorithm on simulated data.
  • HAL:hal-00324133, version 2
  • HAL:http:/​/​hal.archives-ouvertes.fr/​hal-00324133/​en/​
Language
  • English
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