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A Central Limit Theorem for Families of Stochastic Processes Indexed by a Small Average Step Size Parameter, and Some Applications to Learning Models

Published online by Cambridge University Press:  01 January 2025

M. Frank Norman  and
Norma V. Graham
M. Frank Norman
Affiliation:
University of Pennsylvania
Norma V. Graham
Affiliation:
University of Pennsylvania
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Abstract

Let θ > 0 be a measure of the average step size of a stochastic process {pn(θ) }n=1(∞). Conditions are given under which pn(θ) is approximately normally distributed when n is large and θ is small. This result is applied to a number of learning models where θ is a learning rate parameter and pn(θ) is the probability that the subject makes a certain response on the nth experimental trial. Both linear and stimulus sampling models are considered.

Keywords

Stochastic ProcessPublic PolicyLimit TheoremStatistical TheoryCentral Limit
Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 4 , December 1968 , pp. 441 - 449
Copyright
Copyright © 1968 Psychometric Society

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References

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