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 InfoArticle provided by Springer in its journal Annals of the Institute of Statistical Mathematics.
Volume (Year): 63 (2011)
Issue (Month): 4 (August)
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Web page: http://www.springerlink.com/link.asp?id=102845
Other versions of this item:
- Luati, Alessandra & Proietti, Tommaso, 2008. "On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing," MPRA Paper 8910, University Library of Munich, Germany.
- 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
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