On Bather's stochastic approximation algorithm

Rainer Schwabe

Kybernetika (1994)

  • Volume: 30, Issue: 3, page 301-306
  • ISSN: 0023-5954

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Schwabe, Rainer. "On Bather's stochastic approximation algorithm." Kybernetika 30.3 (1994): 301-306. <http://eudml.org/doc/28325>.

@article{Schwabe1994,
author = {Schwabe, Rainer},
journal = {Kybernetika},
keywords = {root; regression function; rate of convergence},
language = {eng},
number = {3},
pages = {301-306},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On Bather's stochastic approximation algorithm},
url = {http://eudml.org/doc/28325},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Schwabe, Rainer
TI - On Bather's stochastic approximation algorithm
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 3
SP - 301
EP - 306
LA - eng
KW - root; regression function; rate of convergence
UR - http://eudml.org/doc/28325
ER -

References

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  1. J. A. Bather, Stochastic approximation: A generalisation of the Robbins-Monro procedure, In: Proc. Fourth Prague Symp. Asymptotic Statistics, Charles Univ. Prague, August 29-September 2, 1988 (P. Mandl and M. Hušková, eds.), Charles Univ., Prague 1989, pp. 13-27. (1988) MR1051424
  2. J. R. Blum, Approximation methods which converge with probability one, Ann. Math. Statist. 25 (1954), 382-386. (1954) Zbl0055.37806MR0062399
  3. K. L. Chung, On a stochastic approximation method, Ann. Math. Statist. 25 (1954), 463-483. (1954) Zbl0059.13203MR0064365
  4. V. Fabian, On asymptotic normality in stochastic approximation, Ann. Math. Statist. 39 (1968), 1327-1332. (1968) Zbl0176.48402MR0231429
  5. G. Kersting, Almost sure approximation of the Robbins-Monro process by sums of independent random variables, Ann. Probab. 5 (1977), 954-965. (1977) Zbl0374.62082MR0494741
  6. L. Ljung, Strong convergence of a stochastic approximation algorithm, Ann. Statist. 6 (1978), 680-696. (1978) Zbl0402.62060MR0464516
  7. B. T. Polyak, New method of stochastic approximation type, Automat. Remote Control 51 (1990), 937-946. (1990) Zbl0737.93080MR1071220
  8. H. Robbins, S. Monro, A stochastic approximation method, Ann. Math. Statist. 22 (1951), 400-407. (1951) Zbl0054.05901MR0042668
  9. D. Ruppert, Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise, Ann. Probab. 10 (1982), 178-187. (1982) Zbl0485.62083MR0637384
  10. D. Ruppert, Efficient Estimators from a Slowly Convergent Robbins-Monro Process, Technical Report No. 781, School of Operations Research and Industrial Engineering, Cornell Univ. Ithaca 1988. (1988) 
  11. D. Ruppert, Stochastic approximation, In: Handbook of Sequential Analysis. (B. K. Ghosh and P. K. Sen, eds.), Marcel Dekker, New York 1991, pp. 503-529. (1991) MR1174318
  12. J. Sacks, Asymptotic distribution of stochastic approximation procedures, Ann. Math. Statist. 29 (1958), 373-405. (1958) Zbl0229.62010MR0098427
  13. R. Schwabe, Strong representation of an adaptive stochastic approximation procedure, Stochastic Process. Appl. 23 (1986), 115-130. (1986) Zbl0614.62107MR0866290
  14. R. Schwabe, Stability results for smoothed stochastic approximation procedures, Z. Angew. Math. Mech. 73 (1993), 639-643. (1993) Zbl0793.65110MR1237850
  15. J. H. Venter, An extension of the Robbins-Monro procedure, Ann. Math. Statist. 38 (1967), 181-190. (1967) Zbl0158.36901MR0205396
  16. H. Walk, Foundations of stochastic approximation, In: Stochastic Approximation and Optimization of Random Systems, DMV Seminar Blauberen, May 28-June 4, 1989 (L. Jung, G. Pflug and H. Walk, eds.), DMV Seminar, Vol. 17, Birkhäuser, Basel 1992, pp. 1-51. (1989) 

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