Edgeworth expansions for stochastic approximation theory |
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Authors: | J Dippon |
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Institution: | (1) Institut für Stochastik und Anwendungen, Univ. Stuttgart, 70550 Stuttgart, Germany |
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Abstract: | To estimate the root ϑ of an unknown regression function f: ℝ → ℝ the iterative Robbins-Monro method X
n+1 = X
n
− a/nY
n
with noisy observations Y
n
= f(X
n
) + V
n
of f(X
n
) can be used. It is well known that X
n
− ϑ can be approximated by a weighted sum of the observation errors V
n
. As recently shown this approximation can be improved by adding quadratic and cubic forms in the observation errors. This
paper presents valid Edgeworth expansions of the distribution function of the approximating sequence up to a remainder term
of order o(1/√n) or even o(1/n).
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Keywords: | stochastic approximation Robbins-Monro procedure Edgeworth expansion |
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