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Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes

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  • John W. 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 W. 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: https://cirano.qc.ca/files/publications/2011s-57.pdf
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    References listed on IDEAS

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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.
    2. John Galbraith & Douglas Hodgson, 2015. "Innovation, experience and artists’ age-valuation profiles: evidence from eighteenth-century rococo and neoclassical painters," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 39(3), pages 259-275, August.

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