Bootstrap Confidence Sets for Spectral Projectors of Sample Covariance

Arbeitspapier

Let X1, . . . ,Xn be i.i.d. sample in Rp with zero mean and the covariance matrix . The problem of recovering the projector onto an eigenspace of from these observations naturally arises in many applications. Recent technique from [9] helps to study the asymp- totic distribution of the distance in the Frobenius norm kPr - bP rk2 between the true projector Pr on the subspace of the rth eigenvalue and its empirical counterpart bP r in terms of the effective rank of . This paper offers a bootstrap procedure for building sharp confidence sets for the true projector Pr from the given data. This procedure does not rely on the asymptotic distribution of kPr - bP rk2 and its moments. It could be applied for small or moderate sample size n and large dimension p. The main result states the validity of the proposed procedure for finite samples with an explicit error bound for the er- ror of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high-dimensional spaces. Numeric results confirm a good performance of the method in realistic examples.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: IRTG 1792 Discussion Paper ; No. 2018-024

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Mathematical and Quantitative Methods: General

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Naumov, A. ; Spokoiny, V. ; Ulyanovk, V.
• Ereignis: Veröffentlichung
• (wer): Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"
• (wo): Berlin
• (wann): 2018

Weitere Informationen

• Handle: http://hdl.handle.net/10419/230735
• Letzte Aktualisierung: 10.03.2025, 11:46 MEZ