Eigen vector perturbation analysis plays a vital role in various statistical data science applications . The proposed estimators are nearly minimax optimaleven when the associated eigen-gap is substantially smaller than what is required in prior theory . In order to mitigate a non-negligible bias issue inherent to thenatural “plug-in” estimator, we develop de-biased estimators that (1) achieveminimax lower bounds for a family of scenarios (modulo some logarithmicfactor) and (2) can be computed in a data-driven manner without samplesplitting. Noteworthily, the proposed estimator are nearly optimaleVEN when the . associated eigraphic eigrams are substantially smaller .

Author(s) : Gen Li, Changxiao Cai, Yuantao Gu, H. Vincent Poor, Yuxin Chen

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Keywords : eigen - estimator - data - smaller - substantially -

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