An Application of Chung's Lemma to the Kiefer-Wolfowitz Stochastic Approximation Procedure
Derman, Cyrus
Ann. Math. Statist., Tome 27 (1956) no. 4, p. 532-536 / Harvested from Project Euclid
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Let $M(x)$ be a strictly increasing regression function for $x < \theta$, and strictly decreasing regression function for $x > \theta$. Under conditions 1, 2, and 3 given below, the stochastic approximation procedure proposed by Kiefer and Wolfowitz [3] is shown to converge stochastically to $\theta$. Under the additional conditions 4, 5, 6 given below, the procedure is shown to converge in distribution to the normal distribution. Our method is the one used by Chung [2].
Publié le : 1956-06-14
Classification:  
@article{1177728277,
     author = {Derman, Cyrus},
     title = {An Application of Chung's Lemma to the Kiefer-Wolfowitz Stochastic Approximation Procedure},
     journal = {Ann. Math. Statist.},
     volume = {27},
     number = {4},
     year = {1956},
     pages = { 532-536},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177728277}
}

Derman, Cyrus. An Application of Chung's Lemma to the Kiefer-Wolfowitz Stochastic Approximation Procedure. Ann. Math. Statist., Tome 27 (1956) no. 4, pp.  532-536. http://gdmltest.u-ga.fr/item/1177728277/