Rational Quadratic Kriging
Abstract
This article proposes rational quadratic kriging, a kriging estimator that addresses the limitations of existing approaches: the mean reversion issue of ordinary kriging and the diverging variance issue of rational kriging. Through the rational quadratic kernel, we establish a connection between rational quadratic kriging and kernel regression. The connection allows us to prove desirable theoretical properties of the new estimator and further propose a novel estimation procedure that utilizes factor weights from kernel regression. We also derive expressions to enable efficient leave-one-out estimation and conformal prediction. Extensive simulations across both deterministic functions and noisy datasets show significant improvements in both prediction and uncertainty quantification. A fast implementation is available in the open-source R package RQK.
Related
- Torsion groups of rational elliptic curves over ℤp-extensions of quadratic fields: the p≤ 5 case
- Torsion growth of rational elliptic curves over Zp-extensions of quadratic fields
- Quadratic hulls of osculating varieties of rational normal curves
- Rational points of exact period three for the quadratic family
- Kriging and Gaussian processes: interconnected frameworks for spatial modelling and prediction
BibTeX
@misc{song2026rational,
title = {{Rational Quadratic Kriging}},
author = {Difan Song and V. Roshan Joseph},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18077},
eprint = {2610.18077},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18077},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Rational Quadratic Kriging
AU - Difan Song
AU - V. Roshan Joseph
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18077
UR - https://arxiv.org/abs/2610.18077
AB - This article proposes rational quadratic kriging, a kriging estimator that addresses the limitations of existing approaches: the mean reversion issue of ordinary kriging and the diverging variance issue of rational kriging. Through the rational quadratic kernel, we establish a connection between rational quadratic kriging and kernel regression. The connection allows us to prove desirable theoretical properties of the new estimator and further propose a novel estimation procedure that utilizes factor weights from kernel regression. We also derive expressions to enable efficient leave-one-out estimation and conformal prediction. Extensive simulations across both deterministic functions and noisy datasets show significant improvements in both prediction and uncertainty quantification. A fast implementation is available in the open-source R package RQK.
ER -