A note on the conditional moments of a multivariate normal distribution confined to a convex set |
| |
Authors: | Shelby J Haberman |
| |
Institution: | Department of Statistics, University of Chicago, Chicago, Illinois 60637 USA |
| |
Abstract: | Let Y be an N(μ, Σ) random variable on Rm, 1 ≤ m ≤ ∞, where Σ is positive definite. Let C be a nonempty convex set in Rm with closure . Let (·,-·) be the Eculidean inner product on Rm, and let μc be the conditional expected value of Y given Y ∈ C. For v ∈ Rm and s ≥ 0, let βs(v) be the expected value of |(v, Y) ? (v, μ)|s and let γs(v) be the conditional expected value of |(v, Y) ? (v, μc)|s given Y ∈ C. For s ≥ 1, γs(v) < βs(v) if and only if , and γs(v) < βs(v) for all v ≠ 0 if and only if for any v ∈ Rm such that v ≠ 0. |
| |
Keywords: | 62H10 60D05 Normal distributions moments convex sets inequalities |
本文献已被 ScienceDirect 等数据库收录! |
|