Exact Covariance Structure and Efficient Computation for L-Comoments
Abstract
L-moments are useful summary statistics and so have been widely employed in statistical analysis. L-comoments provide a multivariate generalization of L-moments. Joint finite-sample covariance structure, which represents the sampling uncertainty, of L-comoments is less well understood than that of univariate L-moments. We thus derive exact finite-sample covariance formulas for sample L-comoments using explicit conditional U-statistic kernels. We further construct an asymptotic projection estimator and an unbiased estimator of the finite-sample covariance matrix and develop positive-definite corrections. An efficient rank-prefix algorithm evaluates the full unbiased covariance estimator in O(n2) time without enumerating disjoint subsets. Numerical experiments demonstrate substantial computational savings. The results provide a basis for first-order covariance approximations for L-comoment ratios and for subsequent multivariate L-moment estimation.
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BibTeX
@misc{seenoi2026exact,
title = {{Exact Covariance Structure and Efficient Computation for L-Comoments}},
author = {Palakorn Seenoi and Jeong-Soo Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28387},
eprint = {2610.28387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28387},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Exact Covariance Structure and Efficient Computation for L-Comoments
AU - Palakorn Seenoi
AU - Jeong-Soo Park
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28387
UR - https://arxiv.org/abs/2610.28387
AB - L-moments are useful summary statistics and so have been widely employed in statistical analysis. L-comoments provide a multivariate generalization of L-moments. Joint finite-sample covariance structure, which represents the sampling uncertainty, of L-comoments is less well understood than that of univariate L-moments. We thus derive exact finite-sample covariance formulas for sample L-comoments using explicit conditional U-statistic kernels. We further construct an asymptotic projection estimator and an unbiased estimator of the finite-sample covariance matrix and develop positive-definite corrections. An efficient rank-prefix algorithm evaluates the full unbiased covariance estimator in O(n^2) time without enumerating disjoint subsets. Numerical experiments demonstrate substantial computational savings. The results provide a basis for first-order covariance approximations for L-comoment ratios and for subsequent multivariate L-moment estimation.
ER -