A companion for the kiefer-wolfowitz-blum stochastic approximation algorithm

By Abdelkader Mokkadem, Mariane Pelletier. 2006

75 citations recorded by the source corpus.

A stochastic algorithm for the recursive approximation of the location 6 of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (1952) 462-466] in the univariate framework, and by Blum [Ann. Math. Statist. 25 (1954) 737-744] in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer-Wolfowitz-Blum algorithm, which allows one to simultaneously recursively approximate the size μ of the maximum of the regression function. A precise study of the joint weak convergence rate of both algorithms is given; it turns out that, unlike the location of the maximum, the size of the maximum can be approximated by an algorithm which converges at the parametric rate. Moreover, averaging leads to an asymptotically efficient algorithm for the approximation of the couple (θ, μ).

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dbadedcd7b64913fdf1cfc24772a0c21b5464a87

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method (2014, background): “One says that Condition (6) was introduced by Galambos and Seneta [16] to define regularly varying sequences (see also Bojanic and Seneta [17]) and by Mokkadem and Pelletier [18] in the context of stochastic approximation algorithms.”
The stochastic approximation method for the estimation of a multivariate probability density (2008, methodology): “…(see, among many others, Blum (1954), Fabian (1967), Kushner and Clark (1978), Hall and Heyde (1980), Ruppert (1982), Chen (1988), Spall (1988), Polyak and Tsybakov (1990), Dippon and Renz (1997), Spall (1997), Chen, Duncan and PasikDuncan (1999), Dippon (2003), and Mokkadem and Pelletier (2007a)).”