On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing
AbstractThe paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically, they enable to derive the optimal kernel associated with a particular covariance structure of the measurement error, where optimality has to be intended in the Gauss-Markov sense. For local polynomial regression it is shown that there is a class of covariance structures, associated with non-invertible moving average processes of given orders which yield the the Epanechnikov and the Henderson kernels as the optimal kernels.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 8910.
Date of creation: 30 May 2008
Date of revision:
Local polynomial regression; Epanechnikov Kernel; Non-invertible Moving average processes;
Other versions of this item:
- Alessandra Luati & Tommaso Proietti, 2011. "On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(4), pages 851-871, August.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-06-07 (All new papers)
- NEP-ECM-2008-06-07 (Econometrics)
- NEP-ETS-2008-06-07 (Econometric Time Series)
- NEP-ORE-2008-06-07 (Operations Research)
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