Bernoulli

• Bernoulli
• Volume 19, Number 2 (2013), 409-425.

Statistical inference for discrete-time samples from affine stochastic delay differential equations

Abstract

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.

Article information

Source
Bernoulli, Volume 19, Number 2 (2013), 409-425.

Dates
First available in Project Euclid: 13 March 2013

https://projecteuclid.org/euclid.bj/1363192033

Digital Object Identifier
doi:10.3150/11-BEJ411

Mathematical Reviews number (MathSciNet)
MR3037159

Zentralblatt MATH identifier
06168758

Citation

Küchler, Uwe; Sørensen, Michael. Statistical inference for discrete-time samples from affine stochastic delay differential equations. Bernoulli 19 (2013), no. 2, 409--425. doi:10.3150/11-BEJ411. https://projecteuclid.org/euclid.bj/1363192033

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