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A smoothing stochastic algorithm for quantile estimation
Affiliation:1. Department of Mathematics & Statistics, University of Ottawa, 585 King Edward, Ottawa ON K1N 6N5, Canada;2. School of Mathematics & Statistics, University of Sydney, NSW 2006, Australia;1. Department of Mathematics, University of Beira Interior, Covilhã, Portugal;2. Center of Mathematics of Minho University, Braga, Portugal;1. Department of Statistics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, Republic of Korea;2. Department of Mathematics and Statistics, Lederle Graduate Research Tower, Box 34515, University of Massachusetts Amherst, Amherst, MA, USA;3. Institute of Economic Research, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, Republic of Korea;1. Department of Statistics, Amirkabir University of Technology, Tehran, Iran;2. School of Mathematics, University of Manchester, Manchester, UK;1. Department of Statistics, Central China Normal University, Wuhan 430079, China;2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract:In this paper, we provide the almost-sure convergence and the asymptotic normality of a smooth version of the Robbins–Monro algorithm for the quantile estimation. A Monte Carlo simulation study shows that our proposed method works well within the framework of a data stream.
Keywords:Quantile estimation  Stochastic approximation  Nonparametric estimation  Almost-sure convergence  Asymptotic normality
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