Sparse Rank Regression for Restricted-Access Economic Data

2026-05-05

AI Summary

This work addresses the challenge of performing sparse and robust regression on heavy-tailed economic data distributed across multiple institutions where centralized processing is infeasible and privacy must be preserved. The authors propose Distributed Convolutional Rank Regression (DCRR), which, for the first time, integrates a non-additive U-statistic-type objective into a communication-efficient distributed framework. DCRR constructs a surrogate objective by combining local CRR losses with gradient corrections and employs a two-stage sparse estimation procedure. Theoretical analysis establishes that DCRR enjoys a distributed strong oracle property and consistent model selection. Empirical results demonstrate that under heavy-tailed errors, DCRR significantly outperforms naive divide-and-conquer approaches and closely approximates the performance of the centralized CRR estimator with high accuracy.

Abstract

Empirical research in economics increasingly relies on restricted-access data held by multiple firms or agencies, making it impossible to construct the estimator of interest on the pooled sample. At the same time, heavy-tailed distributions are pervasive in economics and finance outcomes such as prices, expenditures and loan sizes. We study sparse, robust estimation in the restricted-access setting. The infeasible pooled benchmark is convoluted rank regression (CRR), a smooth rank-based estimator designed for heavy-tailed outcomes. Because the CRR criterion is a non-additive U-statistic, existing communication-efficient methods built for additive empirical losses do not directly apply. We propose distributed convoluted rank regression (DCRR), a surrogate criterion built from a single local CRR loss and an aggregated gradient correction, and show that it shares the same population minimizer as the pooled CRR objective. Building on this surrogate, we develop a two-stage sparse procedure: an iterative $l_1$- penalized stage followed by a folded-concave refinement. For the resulting estimator, we establish non-asymptotic error bounds, a distributed strong oracle property, and a distributed criterion for consistent model selection. Simulations and an application to used-car prices show that DCRR closely approximates pooled CRR and improves on naive divide-and-conquer, particularly under heavy-tailed errors.

Problem

• restricted-access data
• heavy-tailed outcomes
• sparse estimation
• rank regression
• distributed estimation

Innovation

• distributed estimation
• convoluted rank regression
• heavy-tailed data
• sparse modeling
• restricted-access data