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Recursive estimators for stationary, strong mixing processes--a representation theorem and asymptotic distributions

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  • Englund, Jan-Eric
  • Holst, Ulla
  • Ruppert, David

Abstract

Many generalizations of the Robbins-Monro process have been proposed for the purpose of recursive estimation. In this paper it is shown that the recursive estimates can be represented as sums of possibly dependent random variables and can therefore be studied using limit theorems for sums. One application which is particularly studied is recursive M-estimators of location and scale for dependent strong mixing sequences.

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  • Englund, Jan-Eric & Holst, Ulla & Ruppert, David, 1989. "Recursive estimators for stationary, strong mixing processes--a representation theorem and asymptotic distributions," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 203-222, April.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:2:p:203-222
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    Cited by:

    1. Teo Sharia, 2014. "Truncated stochastic approximation with moving bounds: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 163-179, July.
    2. Teo Sharia, 2008. "Recursive parameter estimation: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 157-175, June.
    3. Sharia, Teo, 1998. "On the recursive parameter estimation in the general discrete time statistical model," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 151-172, March.

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