分野別セミナー

In this talk, we discuss the Lasso-based principal component analysis for high-dimensional stationary processes. This problem is motivated by the observation that the standard principal component analysis performs poorly when the dimension of the data is large with sparse eigenvector. We deal with stationary time series under suitable mixing conditions and establish the rate of convergence of the Lasso-type estimators of the first eigenvector. We also elucidate the theoretical rate for choosing the tuning parameter in the Lasso-type estimators. The performance of the sparse principal component analysis is demonstrated by numerical simulations.