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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.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2011s-57.

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Date of creation: 01 Sep 2011
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Handle: RePEc:cir:cirwor:2011s-57

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

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References

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  1. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  2. Jan J. J. Groen & George Kapetanios, 2009. "Model selection criteria for factor-augmented regressions," Staff Reports 363, Federal Reserve Bank of New York.
  3. 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.
  4. 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 332-36, August.
  5. 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.
  6. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  7. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  8. 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.
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Cited by:
  1. John Galbraith & Douglas James Hodgson, 2009. "Dimension Reduction and Model Averaging for Estimation of Artists’ Age-Valuation Profiles," CIRANO Working Papers 2009s-41, CIRANO.

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