On the convergence of a stochastic approximation procedure for estimating the quantile criterion in the case of a discontinuous distribution function

On the convergence of a stochastic approximation procedure for estimating the quantile criterion in the case of a discontinuous distribution function

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Article ID: iaor20112613
Volume: 72
Issue: 2
Start Page Number: 283
End Page Number: 288
Publication Date: Feb 2011
Journal: Automation and Remote Control
Authors:
Keywords: stochastic approximation, distribution fitting
Abstract:

We study the almost surely convergence of a stochastic approximation procedure for the quantile criterion estimation. We take into account the case when the distribution function of the loss function has a discontinuity at a point coinciding with the quantile criterion value. We show that the procedure converges to the desired point under known standard assumptions with no additional constraints.

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