Title: Semi-parametric Factor Analysis
- Speaker: Prof. Yuan Liao, Dept. of Mathematics, UMCP
- Date/Time: Thursday, May 8, 2014 - 3:30pm
- Location: Room 1313, Math Building, University of Maryland College Park (directions).
- Sponsor: University of Maryland, Statistics Program (seminar updates).
Abstract:
This paper studies a high-dimensional semi-parametric factor model with nonparametric loading curves that depend on a few observed characteristic variables. We propose a projected principal components method to estimate the unknown factors, loadings, and number of factors. It is shown that after projecting the respond variable onto the sieve space spanned by the characteristic variables, the projected-PC yields a significant improvement on the rates of convergence than the regular methods in classical factor analysis. In particular, consistency can be achieved without a diverging sample size, as long as the dimensionality grows. This demonstrates that the high dimensionality for semi-parametric factor analysis is actually a blessing, and thus the proposed method is useful in the typical high-dimension-low-sample-size situations. In addition, we also propose a new specification test for the nonparametric loading curves, which fills the gap of the testing literature for semi-parametric factor models.
