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Statistica Sinica 25 (2015), 993-1008

SHRINKAGE ESTIMATION OF LARGE DIMENSIONAL
PRECISION MATRIX USING RANDOM MATRIX THEORY
Cheng Wang1,3, Guangming Pan2, Tiejun Tong3 and Lixing Zhu3
1Shanghai Jiao Tong University, 2Nanyang Technological University
and 3Hong Kong Baptist University

Abstract: This paper considers ridge-type shrinkage estimation of a large dimensional precision matrix. The asymptotic optimal shrinkage coefficients and the theoretical loss are derived. Data-driven estimators for the shrinkage coefficients are also conducted based on the asymptotic results from random matrix theory. The new method is distribution-free and no assumption on the structure of the covariance matrix or the precision matrix is required. The proposed method also applies to situations where the dimension is larger than the sample size. Numerical studies of simulated and real data demonstrate that the proposed estimator performs better than existing competitors in a wide range of settings.

Key words and phrases: Large dimensional data, precision matrix, random matrix theory, ridge-type estimator, shrinkage estimation.

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