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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Original Russian Text © Yu.S. Kan, 2011, published in Avtomatika i Telemekhanika, 2011, No. 2, pp. 71–76.
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Kan, Y.S. On the convergence of a stochastic approximation procedure for estimating the quantile criterion in the case of a discontinuous distribution function. Autom Remote Control 72, 283–288 (2011). https://doi.org/10.1134/S000511791102007X
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DOI: https://doi.org/10.1134/S000511791102007X