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Truncated stochastic approximation with moving bounds: convergence

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  • Teo Sharia

Abstract

In this paper we consider a wide class of truncated stochastic approximation procedures. These procedures have three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We establish convergence and consider several examples to illustrate the results. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Teo Sharia, 2014. "Truncated stochastic approximation with moving bounds: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 163-179, July.
    • Handle: RePEc:spr:sistpr:v:17:y:2014:i:2:p:163-179
    DOI: 10.1007/s11203-014-9093-6
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    References listed on IDEAS

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    1. 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.
    2. Tadic, Vladislav, 1997. "Stochastic gradient algorithm with random truncations," European Journal of Operational Research, Elsevier, vol. 101(2), pages 261-284, September.
    3. Teo Sharia, 2010. "Recursive parameter estimation: asymptotic expansion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 343-362, April.
    4. Teo Sharia, 2008. "Recursive parameter estimation: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 157-175, June.
    5. Lelong, Jérôme, 2008. "Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2632-2636, November.
    6. Chen, Han-Fu & Guo, Lei & Gao, Ai-Jun, 1987. "Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 217-231.
    7. 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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    Cited by:

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    2. Abdelhamid Ouakasse & Guy Mélard, 2017. "A New Recursive Estimation Method for Single Input Single Output Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 417-457, May.

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