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TCA: High Dimensional Principal Component Analysis for non-Gaussian Data
Fang Han · Han Liu

Tue Dec 09:50 AM -- 10:10 AM PST @ Harveys Convention Center Floor, CC

We propose a high dimensional semiparametric scale-invariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution family includes many well-known multivariate distributions like multivariate t and logistic and it is extended to the meta-elliptical by Fang (2002) using the copula techniques. In this paper we extend the meta-elliptical distribution family to a even larger family, called transelliptical. We prove that TCA can obtain a near-optimal s(log d/n)^{1/2} estimation consistency rate in the transelliptical distribution family, even if the distributions are very heavy-tailed, have infinite second moments, do not have densities and possess arbitrarily continuous marginal distributions. A feature selection result with explicit rate is also provided. TCA is also implemented in both numerical simulations and large-scale stock data to illustrate its empirical performance. Both theories and experiments confirm that TCA can achieve model flexibility, estimation accuracy and robustness at almost no cost.

Author Information

Fang Han (Johns Hopkins University)
Han Liu (Princeton University)

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