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  • 统计与管理学院2017年学术报告第68期

    【主 题】 Simultaneous Bootstrap Inference with High-Dimensional Data

    【报告人】 Cun-hui Zhang 教授

    Department of Statistics and Biostatistics, Rutgers University

    【时 间】 2017年11月27日(星期一)10:30-11:30

    【地 点】 上海财经大学统计与管理学院大楼1208会议室

    摘 要】We propose bootstrap methodologies for simultaneous inference of low-dimensional parameters with high dimensional data. We focus on simultaneous confidence intervals for individual coefficients in linear regression, although our approach is applicable in much broader contexts. The problem can be solved by de-biasing regularized estimators such as the Lasso. However, the Bonferroni adjustment is overly conservative and asymptotic theory is complicated, especially for non-Gaussian and heteroscedastic errors. We propose residual, wild and empirical bootstrap methodologies for more accurate and robust simultaneous inference and study sample size requirements and other properties of such procedures. Our theory is complemented by many empirical results.