Moderate Deviations for Extreme Eigenvalues of Real-Valued Sample Covariance Matrices

作者：Jiang, Hui; Wang, Shaochen^*; Zhou, Wang

来源：Journal of Theoretical Probability, 2021, 34(2): 791-808.

DOI：10.1007/s10959-020-00999-x

• Sample covariance matrices
• Extreme eigenvalues
• Moderate deviations

Consider the sample covariance matrices of form W=n(-1)CC(inverted perpendicular), where C is a kxn matrix with real-valued, independent and identically distributed (i.i.d.) mean zero entries. When the squares of the i.i.d. entries have finite exponential moments, the moderate deviations for the extreme eigenvalues of Ware investigated as n ->infinity and eitherkis fixed or k ->infinity with some suitable growth conditions. The moderate deviation rate function reveals that the right (left) tail of lambda(max) is more like Gaussian rather than the Tracy-Widom type distribution whenkgoes to infinity slowly.

• 单位
  南京航空航天大学