Asymptotically Independent Estimates in a Structural Linear Model with Measurement Errors

We consider a structural linear regression model with measurement errors. A new parametrization is proposed in which the expectation of the response variable plays the role of a new parameter instead of the intercept. This enables us to form three groups of asymptotically independent estimators in t...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2017-04, Vol.68 (11), p.1741-1755
Main Authors: Kukush, O. H., Tsarehorodtsev, Ya. V., Shklyar, S. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Regression models
Statistics
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Summary:We consider a structural linear regression model with measurement errors. A new parametrization is proposed in which the expectation of the response variable plays the role of a new parameter instead of the intercept. This enables us to form three groups of asymptotically independent estimators in the case where the ratio of variances measurement errors is known and two groups of this kind in the case where variance of the measurement error is known for the regressor. In this case, it is not assumed that the errors and the latent variable are normally distributed.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-017-1324-8