Asymptotic Properties of Extended Least Squares Estimators
Abstract
We analyze the asymptotic properties of estimators
based on optimizing an extended least squares objective function.
This corresponds to maximum likelihood estimation
when the measurements are normally distributed.
These estimators are used in models where there are unknown parameters
in both the mean and variance of measurements.
Our approach is based on the analysis of
optimization estimators.
We prove consistency and asymptotic normality under
the general conditions of independent, but not necessarily identically
distributed, measurement data.
Asymptotic covariance formulas are derived
for the cases where the data are both normally and arbitrarily distributed.
