| Title:
|
On Bather's stochastic approximation algorithm (English) |
| Author:
|
Schwabe, Rainer |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
301-306 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62L20 |
| idZBL:
|
Zbl 0810.62077 |
| idMR:
|
MR1291932 |
| . |
| Date available:
|
2009-09-24T18:47:47Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125170 |
| . |
| Reference:
|
[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. MR 1051424 |
| Reference:
|
[2] J. R. Blum: Approximation methods which converge with probability one.Ann. Math. Statist. 25 (1954), 382-386. Zbl 0055.37806, MR 0062399 |
| Reference:
|
[3] K. L. Chung: On a stochastic approximation method.Ann. Math. Statist. 25 (1954), 463-483. Zbl 0059.13203, MR 0064365 |
| Reference:
|
[4] V. Fabian: On asymptotic normality in stochastic approximation.Ann. Math. Statist. 39 (1968), 1327-1332. Zbl 0176.48402, MR 0231429 |
| Reference:
|
[5] G. Kersting: Almost sure approximation of the Robbins-Monro process by sums of independent random variables.Ann. Probab. 5 (1977), 954-965. Zbl 0374.62082, MR 0494741 |
| Reference:
|
[6] L. Ljung: Strong convergence of a stochastic approximation algorithm.Ann. Statist. 6 (1978), 680-696. Zbl 0402.62060, MR 0464516 |
| Reference:
|
[7] B. T. Polyak: New method of stochastic approximation type.Automat. Remote Control 51 (1990), 937-946. Zbl 0737.93080, MR 1071220 |
| Reference:
|
[8] H. Robbins, S. Monro: A stochastic approximation method.Ann. Math. Statist. 22 (1951), 400-407. Zbl 0054.05901, MR 0042668 |
| Reference:
|
[9] D. Ruppert: Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise.Ann. Probab. 10 (1982), 178-187. Zbl 0485.62083, MR 0637384 |
| Reference:
|
[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. |
| Reference:
|
[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. MR 1174318 |
| Reference:
|
[12] J. Sacks: Asymptotic distribution of stochastic approximation procedures.Ann. Math. Statist. 29 (1958), 373-405. Zbl 0229.62010, MR 0098427 |
| Reference:
|
[13] R. Schwabe: Strong representation of an adaptive stochastic approximation procedure.Stochastic Process. Appl. 23 (1986), 115-130. Zbl 0614.62107, MR 0866290 |
| Reference:
|
[14] R. Schwabe: Stability results for smoothed stochastic approximation procedures.Z. Angew. Math. Mech. 73 (1993), 639-643. Zbl 0793.65110, MR 1237850 |
| Reference:
|
[15] J. H. Venter: An extension of the Robbins-Monro procedure.Ann. Math. Statist. 38 (1967), 181-190. Zbl 0158.36901, MR 0205396 |
| Reference:
|
[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. |
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