IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/2011s-57.html
   My bibliography  Save this paper

Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes

Author

Listed:
  • John Galbraith
  • Victoria Zinde-Walsh

Abstract

Regression models sometimes contain a linear parametric part and a part obtained by reducing the dimension of a larger set of data. This paper considers properties of estimates of the interpretable parameters of the model, in a general setting in which a potentially unbounded set of other variables may be relevant, and where the number of included factors or components representing these variables can also grow without bound as sample size increases. We show that consistent (and asymptotically normal, given further restrictions) estimation of a parameter of interest is possible in this setting. We examine selection of the particular orthogonal directions, using a criterion which takes into account both the magnitude of the eigenvalue and the correlation of the eigenvector with the variable of interest. Simulation experiments show that an implementation of this method may have good finite-sample performance.

Suggested Citation

  • John Galbraith & Victoria Zinde-Walsh, 2011. "Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes," CIRANO Working Papers 2011s-57, CIRANO.
  • Handle: RePEc:cir:cirwor:2011s-57
    as

    Download full text from publisher

    File URL: http://www.cirano.qc.ca/files/publications/2011s-57.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
    2. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    5. Jan J. J. Groen & George Kapetanios, 2009. "Model selection criteria for factor-augmented regressions," Staff Reports 363, Federal Reserve Bank of New York.
    6. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    7. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    8. Farebrother, R W, 1972. "Principal Component Estimators and Minimum Mean Square Error Criteria in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 332-336, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Galbraith, John W. & Hodgson, Douglas J., 2012. "Dimension reduction and model averaging for estimation of artists' age-valuation profiles," European Economic Review, Elsevier, vol. 56(3), pages 422-435.

    More about this item

    Keywords

    Dimension reduction; eigenvector; infinite-dimensional process; orthogonalized regressors;

    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:cir:cirwor:2011s-57. 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: (Webmaster). General contact details of provider: http://edirc.repec.org/data/ciranca.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.