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In linear regression models, predictors based on least squares or on generalized least squares estimators are usually applied which, however, fail in case of multicollinearity. As an alternative biased estimators like ridge estimators, Kuks-Olman estimators, Bayes or minimax estimators are sometimes suggested. In our analysis the relative instead of the generally used absolute squared error enters...
Abstract: The present article deals with the problem of estimation of parameters in a linear regression model when some data on response variable is missing and the responses are equi-correlated. The ordinary least squares and optimal homogeneous predictors are employed to find the imputed values of missing observations. Their efficiency properties are analyzed using the small disturbances asymptotic...
We propose a least median of absolute (LMA) estimator for a linear regression model, based on minimizing the median absolute deviation of the residuals. Under some regularity conditions on the design points and disturbances, the strong convergence rate of the LMA estimator is established.
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