Prediction in polynomial errors-in-variables models
- 25 May 2020
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (2), 203-219
- https://doi.org/10.15559/20-vmsta154
Abstract
A nmultivariate 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.Keywords
This publication has 9 references indexed in Scilit:
- Consistency of the total least squares estimator in the linear errors-in-variables regressionModern Stochastics: Theory and Applications, 2018
- Errors-in-Variables Methods in System IdentificationPublished by Springer Science and Business Media LLC ,2018
- Convergence of estimators in the polynomial measurement error modelTheory of Probability and Mathematical Statistics, 2016
- Consistency and asymptotic normality for a nonparametric prediction under measurement errorsJournal of Multivariate Analysis, 2015
- Measurement Error in Nonlinear ModelsPublished by Taylor & Francis Ltd ,2006
- Linear Regression AnalysisWiley Series in Probability and Statistics, 2003
- A Companion to Theoretical EconometricsPublished by Wiley ,2003
- Polynomial Regression With Errors in the VariablesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1998
- The Total Least Squares ProblemPublished by Society for Industrial & Applied Mathematics (SIAM) ,1991