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Title: Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes
Authors: Galbraith, John
Zinde-Walsh, Victoria
Issue Date: 2011-09
Publisher: Centre interuniversitaire de recherche en analyse des organisations (CIRANO)
Series/Report no.: Série scientifique (CIRANO);2011s-57
Scientific series (CIRANO);2011s-57
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.
URI: http://www.cirano.qc.ca/pdf/publication/2011s-57.pdf
https://depot.erudit.org/id/003627dd
ISSN: 1198-8177
Appears in Collections:Cahiers scientifiques

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