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Functional convergence of stochastic integrals with application to statistical inference

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  • Davis, Richard A.
  • Song, Li
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    Abstract

    Assuming that {(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV in the space C(R), where fn(β,u,v) is a sequence of “smooth” functions converging to f(β,u,v). Integrals of this form arise as the objective function for inference about a parameter β in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of β which optimizes the objective function. We illustrate this with a moving average process.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 3 ()
    Pages: 725-757

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:725-757

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    Related research

    Keywords: Weak convergence; Stochastic processes; Unit root problem;

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    1. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(01), pages 1-29, March.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
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