On the Kiefer-Wolfowitz approximation method
نویسندگان
چکیده
منابع مشابه
A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm
A stochastic algorithm for the recursive approximation of the location θ of a maximum of a regression function has been introduced by Kiefer and Wolfowitz (1952) in the univariate framework, and by Blum (1954) in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer-Wolfowitz-Blum algorithm, which allows to simultaneously recursively approximate the size...
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We consider the Kiefer-Wolfowitz (KW) stochastic approximation algorithm and derive general upper bounds on its meansquared error. The bounds are established using an elementary induction argument and phrased directly in the terms of tuning sequences of the algorithm. From this we deduce the nonnecessity of one of the main assumptions imposed on the tuning sequences by Kiefer and Wolfowitz [Kie...
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The Dvoretzky–Kiefer–Wolfowitz (DKW) inequality says that if Fn is an empirical distribution function for variables i.i.d. with a distribution function F , and Kn is the Kolmogorov statistic √ n supx |(Fn − F )(x)|, then there is a finite constant C such that for any M > 0, Pr(Kn > M) ≤ C exp(−2M2). Massart proved that one can take C = 2 (DKWM inequality) which is sharp for F continuous. We con...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1957
ISSN: 0528-2195
DOI: 10.21136/cpm.1957.117235