IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/8910.html
   My bibliography  Save this paper

On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing

Author

Listed:
  • Luati, Alessandra
  • Proietti, Tommaso

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 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.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:8910
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/8910/1/MPRA_paper_8910.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Frederick R. Macaulay, 1931. "Appendices to "The Smoothing of Time Series"," NBER Chapters,in: The Smoothing of Time Series, pages 118-169 National Bureau of Economic Research, Inc.
    3. Frederick R. Macaulay, 1931. "The Smoothing of Economic Time Series, Curve Fitting and Graduation," NBER Chapters,in: The Smoothing of Time Series, pages 31-42 National Bureau of Economic Research, Inc.
    4. Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
    5. Kramer, Walter & Hassler, Uwe, 1998. "Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated," Economics Letters, Elsevier, vol. 60(3), pages 285-290, September.
    6. McAleer, Michael, 1992. "Efficient Estimation: The Rao-Zyskind Condition, Kruskal's Theorem and Ordinary Least Squares," The Economic Record, The Economic Society of Australia, vol. 68(200), pages 65-72, March.
    7. Frederick R. Macaulay, 1931. "Introduction to "The Smoothing of Time Series"," NBER Chapters,in: The Smoothing of Time Series, pages 17-30 National Bureau of Economic Research, Inc.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Local polynomial regression; Epanechnikov Kernel; Non-invertible Moving average processes;

    JEL classification:

    • 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; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.