On a stochastic approximation procedure based on averaging

Metrika

Volumn 44, Issue 1, 1996, Pages 165-180

  Schwabe, Rainer ^a   Walk, Harro ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Averaging; Robbins Monro process; Stochastic approximation

Indexed keywords

EID: 0040475877     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02614063     Document Type: Article

References (22)

1. Bather JA (1989) Stochastic approximation: A generalisation of the Robbins-Monro procedure. In: Mandl P, Hušková M (eds) Proc Fourth Prague Symp Asymptotic Statistics Charles Univ Prague August 29-September 2 1988. Charles Univ Prague 13-27
2. Blum JR (1954) Approximation methods which converge with probability one. Ann Math Statist 25:382-386
3. Chung KL (1954) On a stochastic approximation method. Ann Math Statist 25:463-483
4. Derman C, Sacks J (1959) On Dvoretzky's stochastic approximation theorem. Ann Math. Statist 30:601-606
5. Fabian V (1968) On asymptotic normality in stochastic approximation. Ann Math Statist 39:1327-1332
6. Kersting G (1977) Almost sure approximation of the Robbins-Monro process by sums of independent random variables. Ann Probab 5:954-965
7. Ljung L (1978) Strong convergence of a stochastic approximation algorithm. Ann Statist 6:680-696
8. Loève M (1977) Probability theory I. 4th ed. Springer New York
9. Petrov VV (1975) Sums of independent random variables. Springer New York
10. Philipp W, Stout W (1975) Almost sure invariance principles for partial sums of weakly dependent random variables. Mem Am Math Soc 161
11. Polyak BT (1990) New method of stochastic approximation type. Autom Remote Control 51:937-946
12. Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Statist 22:400-407
13. Ruppert D (1982) Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise. Ann Probab 10:178-187
14. Ruppert D (1988) Efficient estimators from a slowly convergent Robbins-Monro process. Technical Report 781, School of Operations Research and Industrial Engineering, Cornell Univ Ithaca
15. Ruppert D (1991) Stochastic approximation. In: Ghosh BK, Sen PK (eds) Handbook of Sequential Analysis. Marcel Dekker New York 503-529
16. Sacks J (1958) Asymptotic distribution of stochastic approximation procedures. Ann Math Statist 29:373-405
17. Schwabe R (1986) Strong representation of an adaptive stochastic approximation procedure. Stochastic Process Appl 23:115-130
18. Schwabe R (1993) Stability results for smoothed stochastic approximation procedures. Z angew Math Mech 73:639-643
19. Schwabe R (1994) On Bather's stochastic approximation procedure. Kybernetika 30:301-306
20. Venter JH (1967) An extension of the Robbins-Monro procedure. Ann Math Statist 38:181-190
21. Walk H (1992) Foundations of stochastic approximation. In: Ljung L, Pflug G, Walk H Stochastic approximation and optimization of random systems. DMV Seminar Blaubeuren, May 28-June 4, 1989 DMV Seminar Vol 17, Birkhäuser Basel 1-51
22. Yin G, Yin K (1994) Asymptotically optimal rate of convergence of smoothed stochastic recursive algorithms. Stochastics Stochastics Rep 47:21-46