Simultaneous estimation of log-normal means: Shrinkage and pretest strategies

Music City Center 

We consider the problem of pooling means from multiple random samples from lognormal
populations. Under the homogeneity assumption of means that all mean values
are equal, we propose improved large sample asymptotic methods for estimating
p log-normal population means when multiple samples are combined. Accordingly,
we suggest estimators based on linear shrinkage, pretest, and Stein-type methodology,
and consider the asymptotic properties using asymptotic distributional bias and
risk expressions. We also present a simulation study to validate the performance of
the suggested estimators based on the simulated relative efficiency. Historical data
from finance and weather are used to in the application of the proposed estimators.

Homogeneity

Pretest estimators

Stein-type estimators

Asymptotic bias and risk 

Section on Statistical Computing