Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
A comparative study for two newly developed estimators for the slope in functional EIV linear model
A. A. Al-Sharadqah
Abstract: Two estimators were recently developed in  for the slope of a line in the functional EIV model. Both are unbiased, up to order sigma^4, where sigma is the error standard deviation. One estimator was constructed as a function of the maximum likelihood estimator (MLE). Therefore, it was called Adjusted MLE (AMLE). The second estimator was constructed in a completely different approach. Although both the estimators are unbiased, up to the order sigma^4, the latter estimator is much more accurate than the AMLE. We study here these two estimators more rigorously, and we show why one estimator outperforms the other one.
Keywords: Simple linear regression, Errors-in-Variables models, small-noise model, maximum likelihood estimator, bias correction, mean squared errors.
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