Luati, Alessandra and Proietti, Tommaso (2008): On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing.

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Abstract
The 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 GaussMarkov sense. For local polynomial regression it is shown that there is a class of covariance structures, associated with noninvertible moving average processes of given orders which yield the the Epanechnikov and the Henderson kernels as the optimal kernels.
Item Type:  MPRA Paper 

Original Title:  On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing 
Language:  English 
Keywords:  Local polynomial regression; Epanechnikov Kernel; Noninvertible Moving average processes 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  8910 
Depositing User:  Tommaso Proietti 
Date Deposited:  30. May 2008 22:20 
Last Modified:  14. Feb 2013 18:56 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/8910 