ASYMPTOTIC DISTRIBUTION OF UNBIASED LINEAR ESTIMATORS IN
THE PRESENCE OF HEAVY-TAILED STOCHASTIC REGRESSORS AND
RESIDUALS
Gennady Samorodnitsky
Svetlozar T. Rachev
Jeong-Ryeol Kurz-Kim
Stoyan V. Stoyanov
Abstract: Under the symmetric -stable
distributional assumption for the disturbances, Blattberg and Sargent [3] consider unbiased
linear estimators for a regression model with non-stochastic regressors. We study both the
rate of convergence to the true value and the asymptotic distribution of the normalized error
of the linear unbiased estimators. By doing this, we allow the regressors to be stochastic
and disturbances to be heavy-tailed with either finite or infinite variances, where
the tail-thickness parameters of the regressors and disturbances may be different.
2000 AMS Mathematics Subject Classification: Primary: 62J05; Secondary:
60E07.
Key words and phrases: Asymptotic distribution, rate of convergence, stochastic
regressor, stable non-Gaussian, finite or infinite variance, heavy tails.