PreprintCC BY-NC-ND 4.0arXiv
Difference-based variance estimators with repeated measurements
Abstract
In this paper, we formulate a general differencing framework for variance estimation across a range of settings. We demonstrate that conventional difference-based noise variance estimators cannot achieve the desired bias-correcting power in nonparametric regression with repeated measurements. A new high-order bias-corrected differencing scheme, adapted to repeated measurements, is proposed by interlacing inter-group and intra-group differencing. The theoretical properties of the new sequences and estimators are studied. Our proposals are particularly efficient in finite samples and under high signal-to-noise ratio scenarios, where asymptotic convergence has not yet fully taken effect, due to their strong bias-correcting power.
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BibTeX
@misc{lee2026differencebased,
title = {{Difference-based variance estimators with repeated measurements}},
author = {Chak Ming Lee and Kin Wai Chan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34748},
eprint = {2609.34748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34748},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Difference-based variance estimators with repeated measurements
AU - Chak Ming Lee
AU - Kin Wai Chan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34748
UR - https://arxiv.org/abs/2609.34748
AB - In this paper, we formulate a general differencing framework for variance estimation across a range of settings. We demonstrate that conventional difference-based noise variance estimators cannot achieve the desired bias-correcting power in nonparametric regression with repeated measurements. A new high-order bias-corrected differencing scheme, adapted to repeated measurements, is proposed by interlacing inter-group and intra-group differencing. The theoretical properties of the new sequences and estimators are studied. Our proposals are particularly efficient in finite samples and under high signal-to-noise ratio scenarios, where asymptotic convergence has not yet fully taken effect, due to their strong bias-correcting power.
ER -