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Matrix variance for covariance estimation
Definition
For a random vector with mean and covariance as in Covariance matrix of a finite-dimensional random vector, assume . Its matrix variance is When , define the intrinsic ratio
The expectation is entrywise. The finite fourth moment makes every entry integrable. This definition imposes neither Huber contamination nor sample replacement.
Depends on
Used by
- Adaptive truncated covariance estimator Algorithm
- Intrinsic matrix variance alone does not control pilot-centered covariance truncation Counterexample
- Matrix variance need not dominate trace covariance times operator norm Counterexample
- A polynomial-tail law with finite matrix variance Example
- Fixed-scale matrix-truncated covariance deviation under finite matrix variance Lemma
- Lepski scale selection transfers fixed-scale covariance bounds Lemma
- Oracle-truncated covariance and vector concentration under finite matrix variance Lemma
- The covariance matrix variance ratio is at least one Lemma
- Adaptive truncated covariance has a finite matrix-variance operator bound Theorem
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Stanislav Minsker and Xiaohan Wei, Estimation of the Covariance Structure of Heavy-Tailed Distributions, §2 (standard reference, not scraped)