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TCA: High Dimensional Principal Component Analysis for non-Gaussian Data
Published on Jan 16, 20135948 Views
We propose a high dimensional semiparametric scaleinvariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal c
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Chapter list
Transelliptical Component Analysis00:00
General Framework00:12
Outline00:48
Sparse Principal Component Analysis01:12
Leading Eigenvectors Estimation01:18
Applications01:48
Sparse Leading Eigenvectors02:09
Assumption and Estimation03:02
Rates of Convergence03:54
Constraints05:06
Equity Data05:17
Extensions to non-Gaussian (Abnormal)06:03
Liu, Lafferty and Wasserman (2009, JMLR) (1)06:29
Liu, Lafferty and Wasserman (2009, JMLR) (2)07:12
Liu et.al. Annals of Statistics (2012)07:32
Good Enough?08:30
Lehman Brothers09:29
Elliptical Distribution10:02
Transelliptical Distribution11:13
Kendall’s tau and Its Invariance Property12:02
Transelliptical Component Analysis12:46
Theoretical Results13:11
Equity Data Again13:35
Beyond PCA14:20
Remarks14:45
Thanks!14:58