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Convergence of stochastic approximation algorithms under irregular conditions

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  • Jian Zhang
  • Faming Liang

Abstract

We consider a class of stochastic approximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locally Lipschitz continuous. Here, we show that this condition can be relaxed to the extent that the estimating functions are bounded and continuous almost everywhere. As a consequence, the use of the SA algorithm can be extended to some problems with irregular estimating functions. Our theoretical results are illustrated by solving an estimation problem for exponential power mixture models.

Suggested Citation

  • Jian Zhang & Faming Liang, 2008. "Convergence of stochastic approximation algorithms under irregular conditions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(3), pages 393-403, August.
    • Handle: RePEc:bla:stanee:v:62:y:2008:i:3:p:393-403
    DOI: 10.1111/j.1467-9574.2008.00397.x
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    References listed on IDEAS

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    1. L. Tian & J. Liu & Y. Zhao & L. J. Wei, 2004. "Statistical inference based on non-smooth estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 943-954, December.
    2. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
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    Cited by:

    1. Paolo Giordani & Xiuyan Mun & Robert Kohn, 2012. "Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 154-192, December.

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