On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing
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 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.
|Date of creation:||30 May 2008|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Peter C.B. Phillips & Joon Y. Park, 1986. "Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors," Cowles Foundation Discussion Papers 802, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B., 1992. "Geometry of the Equivalence of OLS and GLS in the Linear Model," Econometric Theory, Cambridge University Press, vol. 8(01), pages 158-159, March.
- Kramer, Walter & Hassler, Uwe, 1998.
"Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated,"
Elsevier, vol. 60(3), pages 285-290, September.
- Krämer, Walter & Hassler, Uwe, 1997. "Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated," Technical Reports 1997,01, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Wallis, Kenneth F, 1981. "Models for X-11 and 'X-11-Forecast' Procedures for Preliminary and Revised Seasonal Adjustments," The Warwick Economics Research Paper Series (TWERPS) 198, University of Warwick, Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:8910. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.