A Decision Theoretic Approach to a Stochastic Approximation Problem.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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The problem of approximating the root of a linear function with unit slope is investigated. The error random variables are assumed to be independent and identically distributed standard normal random variables. A stochastic approximation procedure is characterized as a sequence of decision functions corresponding to a particular sequence of statistical decision problems. Bayes procedures are characterized and convergence is proved. The harmonic Robbins-Monro procedure is shown to correspond to a sequence of natural decision functions. A more general approximation problem is also considered. Author
- Statistics and Probability