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Gaussian sample-covariance operator-norm bound
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Variance
Covariance
Covariance matrix
Sample mean and covariance
Sample covariance matrix
Effective rank of a covariance matrix
2026-09-28
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For independent centered Gaussian
vectors
with
covariance
Σ
and uncentered sample
covariance
Σ
=
n
−
1
∑
i
x
i
x
i
T
, with
probability
at least
1
−
e
−
t
,
∥
Σ
−
Σ
∥
op
≤
C
∥
Σ
∥
op
(
n
r
(
Σ
)
+
t
+
n
r
(
Σ
)
+
t
)
.
(1)
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(12)
Effective rank of a covariance matrix
Sample covariance matrix
Sample mean and covariance
Covariance matrix
Covariance
Variance
Expected value
Probability theory
Probability and statistics
Area of mathematics
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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