CENTRAL LIMIT THEOREM FOR GRAM-SCHMIDT RANDOM WALK DESIGN
成果类型：
Article
署名作者：
Chatterjee, Sabyasachi; Dey, Partha S.; Goswami, Subhajit
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign; Tata Institute of Fundamental Research (TIFR)
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/25-AAP2147
发表日期：
2025
页码：
1407-1441
关键词：
摘要：
We prove a central limit theorem for the Horvitz-Thompson estimator based on the Gram-Schmidt walk (GSW) design, recently developed in Harconsider the version of GSW design, which uses a randomized pivot order. We deduce our result under very mild assumptions involving only the problem parameters, such as the (sum) potential outcome vector and the covariate matrix. As a very important consequence of our analysis, we obtain the precise limiting variance of the estimator in terms of these parameters, which is smaller than the previously known upper bound. The main ingredients are a simplified skeletal process approximating the GSW design and concentration phenomena for random matrices obtained from random sampling using Stein's method for exchangeable pairs.
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