Estimator using the geometric mean

Geometric Mean Estimator

https://arxiv.org/abs/1804.03989

The geometric mean can be used to estimate the scale of a Coupled Gaussian. Shown is comparison of the estimates for the variance of Gaussian distribution and the scale of a Cauchy Distribution. A proof is provided showing the relationship between the geometric mean of the coupled Gaussian distributions and the scale of the distributions.  Numerical evidence is provided that for a wide range of tail decay the estimator is unbiased and has diminishing variance as the number of samples increases.

View all posts