JSM 2012 Home

## JSM 2012 Online Program

The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.

Online Program Home

#### Abstract Details

 Activity Number: 15 Type: Topic Contributed Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM Sponsor: Section on Statistical Learning and Data Mining Abstract - #304456 Title: General Consistency Results of PCA in High Dimension Author(s): Sungkyu Jung*+ and J. Steve Marron and Jason Fine Companies: University of Pittsburgh and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill Address: 2734 Cathedral of Learning, Pittsburgh, PA, 15260, United States Keywords: Abstract: Principal component Analysis is a widely used method for dimensionality reduction and visualization of multidimensional data. It becomes common in modern data analytic situation that the dimension $d$ of the observation is much larger than the sample size $n$. This leads to a new domain in asymptotic studies of the estimated principal component analysis, that is, in terms of the limit of $d$. A unified framework for assessing the consistency of principal component estimates in a wide range of asymptotic settings is provided. In particular, our result works for any ratio of dimension and sample size, $d/n \to c$, $c \in [0,\infty]$. We apply this framework to two different statistical situations. When applied to a factor model, we obtain a unified view on the sufficient condition for the consistency of principal component analysis. We propose to use time-varying principal components to model multivariate longitudinal data with an irregular grid. A sufficient condition for the consistency of the estimates is obtained by the proposed tool. Simulation results and real data analysis are included.

The address information is for the authors that have a + after their name.
Authors who are presenting talks have a * after their name.

2012 JSM Online Program Home

For information, contact jsm@amstat.org or phone (888) 231-3473.