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

Uwe Küchler; Michael Sørensen

doi:10.3150/11-BEJ411

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

Uwe Küchler, Michael Sørensen

Institut for Matematiske Fag

4 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Bernoulli
Vol/bind	19
Udgave nummer	2
Sider (fra-til)	409 - 425
ISSN	1350-7265
DOI	https://doi.org/10.3150/11-BEJ411
Status	Udgivet - maj 2013

Adgang til dokumentet

10.3150/11-BEJ411

Citationsformater

@article{0270d6c39ed44c7db3ae0c1c24995d27,

title = "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. ",

author = "Uwe K{\"u}chler and Michael S{\o}rensen",

year = "2013",

month = may,

doi = "10.3150/11-BEJ411",

language = "English",

volume = "19",

pages = "409 -- 425",

journal = "Bernoulli",

issn = "1350-7265",

publisher = "International Statistical Institute",

number = "2",

}

TY - JOUR

T1 - Statistical inference for discrete-time samples from affine stochastic delay differential equations

AU - Küchler, Uwe

AU - Sørensen, Michael

PY - 2013/5

Y1 - 2013/5

N2 - 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.

AB - 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.

U2 - 10.3150/11-BEJ411

DO - 10.3150/11-BEJ411

M3 - Journal article

SN - 1350-7265

VL - 19

SP - 409

EP - 425

JO - Bernoulli

JF - Bernoulli

IS - 2

ER -