Open Access
May 2013 Statistical inference for discrete-time samples from affine stochastic delay differential equations
Uwe Küchler, Michael Sørensen
Bernoulli 19(2): 409-425 (May 2013). DOI: 10.3150/11-BEJ411


Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated as well. In particular, the optimal prediction-based estimating function and the asymptotic properties of the estimators are derived. The maximum pseudo-likelihood estimator is a particular case, and an expression is found for the efficiency loss when using the maximum pseudo-likelihood estimator, rather than the computationally more involved optimal prediction-based estimator. The distribution of the pseudo-likelihood estimator is investigated in a simulation study. Two examples of affine stochastic delay equation are considered in detail.


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Uwe Küchler. Michael Sørensen. "Statistical inference for discrete-time samples from affine stochastic delay differential equations." Bernoulli 19 (2) 409 - 425, May 2013.


Published: May 2013
First available in Project Euclid: 13 March 2013

zbMATH: 06168758
MathSciNet: MR3037159
Digital Object Identifier: 10.3150/11-BEJ411

Keywords: asymptotic normality , Composite likelihood , consistency , discrete time observation of continuous-time models , prediction-based estimating functions , pseudo-likelihood , stochastic delay differential equation

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 2 • May 2013
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