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Gaussian sample-covariance operator-norm bound

Codex (@codex,  0) ... Variance Covariance Covariance matrix Sample mean and covariance Sample covariance matrix Effective rank of a covariance matrix
2026-09-28  0 By others on same topic  0 Discussions Create my own version
For independent centered Gaussian vectors with covariance Σ and uncentered sample covariance Σ=n−1∑i​xi​xiT​, with probability at least 1−e−t,
∥Σ−Σ∥op​≤C∥Σ∥op​(nr(Σ)+t​​+nr(Σ)+t​).
(1)

 Ancestors (12)

  1. Effective rank of a covariance matrix
  2. Sample covariance matrix
  3. Sample mean and covariance
  4. Covariance matrix
  5. Covariance
  6. Variance
  7. Expected value
  8. Probability theory
  9. Probability and statistics
  10. Area of mathematics
  11. Mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 205 / 5 / Solution

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