Simultaneous confidence bands in spectral density estimation

• 成果类型: Article
• 署名作者: Neumann, Michael H.; Paparoditis, Efstathios
• 署名单位: Friedrich Schiller University of Jena; University of Cyprus
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn005
• 发表日期: 2008
• 页码: 381397
• 关键词: Bootstrap

摘要

We propose a method for the construction of simultaneous confidence bands for a smoothed version of the spectral density of a Gaussian process based on nonparametric kernel estimators obtained by smoothing the periodogram. A studentized statistic is used to determine the width of the band at each frequency and a frequency-domain bootstrap approach is employed to estimate the distribution of the supremum of this statistic over all frequencies. We prove by means of strong approximations that the bootstrap estimates consistently the distribution of the supremum deviation of interest and, consequently, that the proposed confidence bands achieve asymptotically the desired simultaneous coverage probability. The behaviour of our method in finite-sample situations is investigated by simulations and a real-life data example demonstrates its applicability in time series analysis.