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Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes

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  • 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
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    File URL: http://www.cirano.qc.ca/files/publications/2011s-57.pdf
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    References listed on IDEAS

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    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.
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    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;

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