Table 1 Norms and antinorms
From: Exact inference on scaling parameters in norm and antinorm contoured sample distributions
Parameter | q | ∈[1,∞) | ∈(0,1] | ∈(−∞,0) |
|---|---|---|---|---|
Functional | |.| q | Norm | Antinorm | Semi-antinorm, z≠0 |
Unit ball | B q | Convex | Radially concave | Radially concave |
w.r.t. standard fan in \(\mathbb {R}^{n}\) | w.r.t. standard fan in \(\mathbb {R}^{n}\) | |||
Inverse image of 0 | N q | {0} | {0} | \({\cup _{1}^{d}} H_{i}\) |