Affiliation:
1. Stanford University, Stanford, CA, USA
Abstract
In adaptive importance sampling and other contexts, we have
K
> 1 unbiased and uncorrelated estimates μ
^
k
of a common quantity μ. The optimal unbiased linear combination weights them inversely to their variances, but those weights are unknown and hard to estimate. A simple deterministic square root rule based on a working model that Var(μ
^
k
) ∝
k
−1/2
gives an unbiased estimate of μ that is nearly optimal under a wide range of alternative variance patterns. We show that if Var(μ
^
k
)∝
k
−
y
for an unknown rate parameter
y
∈[0,1], then the square root rule yields 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. Numerical work shows that rule is similarly robust to some other patterns with mildly decreasing variance as
k
increases.
Funder
U.S. National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Science Applications,Modeling and Simulation