ON OPTIMAL BLOCK RESAMPLING FOR GAUSSIAN-SUBORDINATED LONG-RANGE DEPENDENT PROCESSES

• 成果类型: Article
• 署名作者: Zhang, Qihao; Lahiri, Soumendra N.; Nordman, Daniel J.
• 署名单位: Iowa State University; Washington University (WUSTL)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2242
• 发表日期: 2022
• 页码: 3619-3646
• 关键词: sampling window method; time-series; BOOTSTRAP METHODS; variance; CONVERGENCE; estimators; validity; memory

摘要

Block-based resampling estimators have been intensively investigated for weakly dependent time processes, which has helped to inform imple-mentation (e.g., best block sizes). However, little is known about resampling performance and block sizes under strong or long-range dependence. To es-tablish guideposts in block selection, we consider a broad class of strongly dependent time processes, formed by a transformation of a stationary long -memory Gaussian series, and examine block-based resampling estimators for the variance of the prototypical sample mean; extensions to general statistical functionals are also considered. Unlike weak dependence, the properties of resampling estimators under strong dependence are shown to depend intri-cately on the nature of nonlinearity in the time series (beyond Hermite ranks) in addition to the long-memory coefficient and block size. Additionally, the intuition has often been that optimal block sizes should be larger under strong dependence (say O (n1/2) for a sample size n) than the optimal order O (n1/3) known under weak dependence. This intuition turns out to be largely incor-rect, though a block order O(n1/2) may be reasonable (and even optimal) in many cases, owing to nonlinearity in a long-memory time series. While op-timal block sizes are more complex under long-range dependence compared to short-range, we provide a consistent data-driven rule for block selection. Numerical studies illustrate that the guides for block selection perform well in other block-based problems with long-memory time series, such as distri-bution estimation and strategies for testing Hermite rank.