Prediction in polynomial errors-in-variables models
Volume 7, Issue 2 (2020), pp. 203–219
Pub. online: 25 May 2020
Type: Research Article
Open Access
Open Access
Received
24 April 2020
24 April 2020
Revised
4 May 2020
4 May 2020
Accepted
6 May 2020
6 May 2020
Published
25 May 2020
25 May 2020
Abstract
A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.
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