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Asymptotic Properties of Extended Least Squares Estimators

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.

Input File: asymptotic_elsq.omh