The square root rule for adaptive importance sampling

01/10/2019

∙

by   Art B. Owen, et al.

∙

0

∙

share

In adaptive importance sampling, and other contexts, we have unbiased and uncorrelated estimates of a common quantity μ and the variance of the k'th estimate is thought to decay like k^-y for an unknown rate parameter y∈ [0,1]. If we combine the estimates as though y=1/2, then the resulting estimate attains the optimal variance rate with a constant that is too large by at most 9/8 for any 0< y< 1 and any number K of estimates.