Lower bounds for invariant statistical models with applications to principal component analysis

被引：1
作者：
Wahl, Martin [1 ]
机构：
[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2022年 / 58卷 / 03期
关键词：
Covariance operator; Principal components; Lower bounds; Van Trees inequality; Fisher information; Equivariant model; Special orthogonal group; Large deviations; EFFICIENT ESTIMATION; FUNCTIONALS; RATES;
D O I：
10.1214/21-AIHP1193
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper bounds for models with decaying eigenvalues are sharp. The proof relies on lower bound techniques based on group invariance arguments. These techniques can also be applied to a variety of other statistical models.
引用
收藏
页码：1565 / 1589
页数：25
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