Least Hausdorff distance regression for interval-valued data
Holder： Wei Lin（University of International Business and Economics）
Time：2026-04-16 15:10-17:00
Location：Room 217, Guanghua Building 2
Abstract:
This paper develops a new regression methodology for interval-valued data based on the Hausdorff distance, a canonical metric for set-valued random variables. We first show a key equivalence relationship that decomposes the Hausdorff distance between two intervals into a combination of distances between their endpoints, midpoints, and radii, providing a unified foundation for interval regression. We propose the Least Hausdorff Distance (LHD) estimator, which minimizes the sum of Hausdorff distances between observed and predicted intervals. Under assumptions of strict stationarity and alpha-mixing weak dependence, we prove the consistency and asymptotic normality of the LHD estimator using empirical process techniques for mixing sequences. We also construct consistent heteroskedasticity-robust standard errors by combining the Powell quantile difference method for density estimation with a martingale difference sequence simplification of the long-run covariance matrix.
About the Speaker:
林蔚，对外经济贸易大学经济学院教授，博士生导师，于美国加州大学河滨分校获得经济学博士学位，主要研究领域为时间序列分析与非参数计量经济学。研究成果发表在Journal of Econometrics、Journal of Business and Economic Statistics、Journal of Applied Econometrics等国际期刊，其中代表性成果包括区间型数据分析、季节调整方法和空间面板数据模型等。
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