BRACE: Blockwise Rank Aggregation for Correlation Estimation

2026-09-23

AI Summary

为解决Chatterjee估计量在有限复制下的方差问题，提出BRACE方法，通过局部块秩聚合来提高相关性估计的准确性。

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.

Problem

• Chatterjee's estimator
• finite-replication variance gap
• fixed alternatives

Innovation

• Blockwise Rank Aggregation
• Correlation Estimation
• Finite-replication Variance
• Information Bound
• Wald Confidence Intervals