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Bias Reduction using Stochastic Approximation
Author(s) -
Leung Denis HengYan,
Wang YouGan
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00005
Subject(s) - mathematics , variance reduction , independent and identically distributed random variables , statistics , variance (accounting) , sampling bias , reduction (mathematics) , sampling (signal processing) , sample size determination , importance sampling , term (time) , exponential function , random variable , monte carlo method , mathematical analysis , computer science , physics , geometry , accounting , filter (signal processing) , quantum mechanics , business , computer vision
The paper studies stochastic approximation as a technique for bias reduction. The proposed method does not require approximating the bias explicitly, nor does it rely on having independent identically distributed (i.i.d.) data. The method always removes the leading bias term, under very mild conditions, as long as auxiliary samples from distributions with given parameters are available. Expectation and variance of the bias‐corrected estimate are given. Examples in sequential clinical trials (non‐i.i.d. case), curved exponential models (i.i.d. case) and length‐biased sampling (where the estimates are inconsistent) are used to illustrate the applications of the proposed method and its small sample properties.