Functional and random central limit theorems for the Robbins-Munro process

Functional and random central limit theorems for the Robbins-Munro process

A functional central limit theorem extending the central limit theorem of Chung (1954) for the Robbins–Munro procedure is proved. It is shown that the asymptotic normality is preserved under certain random stopping rules.

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Veröffentlicht in:Journal of applied probability 1976-03, Vol.13 (1), p.148-154
1. Verfasser: McLeish, D. L.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Central limit theorem
Conditional probabilities
Martingales
Mathematical procedures
Mathematical theorems
Perceptron convergence procedure
Random variables
Short Communications
Statistical variance
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Zusammenfassung:A functional central limit theorem extending the central limit theorem of Chung (1954) for the Robbins–Munro procedure is proved. It is shown that the asymptotic normality is preserved under certain random stopping rules.
ISSN:0021-9002
1475-6072
DOI:10.2307/3212676