Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2515

 Title: A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples Authors: Jacob, Christine Keywords: Quasi-likelihood estimatorminimum contrast estimatorleast-squares estimatorleast absolute deviation estimatormaximum likelihood estimatoruniform strong law of large numbers for martingalesnonstationary stochastic processstochastic regression, consistencyasymptotic 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. URI: http://hdl.handle.net/10525/2515 ISSN: 0204-9805 Appears in Collections: 2013 Volume 22

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