BRACE: Blockwise Rank Aggregation for Correlation Estimation
Abstract
Chatterjee's estimator uses only two local comparisons per interior observation, leaving a finite-replication variance gap under fixed alternatives. We introduce BRACE, short for blockwise rank aggregation for correlation estimation, which replaces adjacent comparisons with local blocks and averages every within-block rank difference. The block size controls the variance cost of finite local replication. An L2 expansion separates the efficient first-order component of the response-rank statistic from an orthogonal finite-replication component. For an admissible diverging block size, the latter vanishes, so the direct rank estimator attains the information bound. The decomposition yields a consistent variance estimator and Wald confidence intervals under fixed alternatives. At independence, the efficient first-order term vanishes, and the proposed estimator enters a second-order regime in which the same factor controls its null variance.
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BibTeX
@misc{ngou2026brace,
title = {{BRACE: Blockwise Rank Aggregation for Correlation Estimation}},
author = {Man Hei Ngou and Yanran Li and Zhexiao Lin and Zexi Cai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28269},
eprint = {2609.28269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - BRACE: Blockwise Rank Aggregation for Correlation Estimation
AU - Man Hei Ngou
AU - Yanran Li
AU - Zhexiao Lin
AU - Zexi Cai
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28269
UR - https://arxiv.org/abs/2609.28269
AB - Chatterjee's estimator uses only two local comparisons per interior observation, leaving a finite-replication variance gap under fixed alternatives. We introduce BRACE, short for blockwise rank aggregation for correlation estimation, which replaces adjacent comparisons with local blocks and averages every within-block rank difference. The block size controls the variance cost of finite local replication. An L2 expansion separates the efficient first-order component of the response-rank statistic from an orthogonal finite-replication component. For an admissible diverging block size, the latter vanishes, so the direct rank estimator attains the information bound. The decomposition yields a consistent variance estimator and Wald confidence intervals under fixed alternatives. At independence, the efficient first-order term vanishes, and the proposed estimator enters a second-order regime in which the same factor controls its null variance.
ER -