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
