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Title: A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples
Authors: Jacob, Christine
Keywords: Quasi-likelihood estimator
minimum contrast estimator
least-squares estimator
least absolute deviation estimator
maximum likelihood estimator
uniform strong law of large numbers for martingales
nonstationary stochastic process
stochastic regression, consistency
asymptotic distribution
Issue Date: 2013
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Pliska Studia Mathematica Bulgarica, Vol. 22, No 1, (2013), 71p-88p
Abstract: Let {Zn}n∈N be a real stochastic process on (Ω, F, Pθ0), where θ0 is a unknown p-dimensional parameter. We propose a GQLE (Generalized Quasi-Likelihood Estimator) of θ0 based on a single trajectory of the process and defined by ˆθn:=argminθ ∑k=1nΨk(Zk, θ), where Ψk(z, θ) is Fk-1-measurable, {Fn}n being an increasing sequence of σ-algebras. This class of estimators includes many different types of estimators such as conditional least squares estimators, least absolute deviation estimators and maximum likelihood estimators, and allows missing data, outliers, or infinite conditional variance. We give general conditions leading to the strong consistency and the asymptotic normality of ˆθn. The key tool is a uniform strong law of large numbers for martingales. We illustrate the results in the branching processes setting
Description: 2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.
ISSN: 0204-9805
Appears in Collections:2013 Volume 22

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