Asymptotic behavior of truncated stochastic approximation procedures

Teo Sharia, Lei Zhong

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We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. In particular, we show that under quite mild conditions, stochastic approximation procedures are asymptotically linear in the statistical sense, that is, they can be represented as weighted sums of random variables. Therefore, a suitable form of the central limit theorem can be applied to derive asymptotic distribution of the corresponding processes. The theory is illustrated by various examples and special cases.
Original languageEnglish
Pages (from-to)37-54
Number of pages18
JournalMathematical Methods of Statistics
Issue number1
Publication statusPublished - 26 May 2017

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