Year: 2026
Type: preprint
Abstract: The multivariate expectile-based distribution is a `spiked' perturbation of a multivariate Gaussian distribution, proposed by Arbel et al. in 2023. The rejection sampler proposed for this distribution in the initial work is valid, but its acceptance probability can degenerate badly both in high dimension and in the strongly asymmetric limit. We give a simple alternative. After affine whitening and a polar decomposition, the sampling problem reduces exactly to a univariate distribution, and an additional hyperbolic change of variables exhibits this distribution as log-concave, so that a universal and uniformly efficient construction of Devroye applies. The resulting exact sampler therefore enjoys an acceptance probability of at least $1 - \exp \left( -1 \right) = 0.632120 \ldots$, uniformly over the dimension and all admissible asymmetry parameters.
Source: arXiv (Cornell University)
Author: Power, Sam
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214151002