A Uniformly Efficient Rejection Sampler for the Multivariate Expectile-Based Distribution
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 ( −1 ) = 0.632120 …, uniformly over the dimension and all admissible asymmetry parameters.
Related
- Query-Efficient Rejection Sampling for Parallel Masked Diffusion
- Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations
- A Mathai-type Multivariate Nakagami-m Distribution: Density, Closed-form Estimators, and Asymptotic Efficiency
- Improved estimation of differential entropy of a multivariate Gaussian distribution
- Quantiles for multivariate distribution: a short survey of population concepts
BibTeX
@misc{power2026uniformly,
title = {{A Uniformly Efficient Rejection Sampler for the Multivariate Expectile-Based Distribution}},
author = {Sam Power},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27885},
eprint = {2609.27885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27885},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Uniformly Efficient Rejection Sampler for the Multivariate Expectile-Based Distribution
AU - Sam Power
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27885
UR - https://arxiv.org/abs/2609.27885
AB - 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 ( −1 ) = 0.632120 …, uniformly over the dimension and all admissible asymmetry parameters.
ER -