谱密度积分的自归一化
Self-normalization for Spectral Density Integrals
- Ruhr University Bochum（波鸿鲁尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对线性过程谱密度积分的估计量，建立了其自归一化过程的弱收敛性，明确线性与非线性泛函自归一化极限分布的差异，以积分平方谱密度为例验证了非线性泛函的特殊现象。
AI中文摘要：
谱密度的积分常被用于总结线性过程的谱特性。本研究针对基于序列周期图的此类积分估计量，探讨其自归一化问题，并建立了对应过程的弱收敛性。对于谱密度的线性泛函，自归一化可产生不受未知谱量影响的枢轴极限分布；但对于非线性泛函，极限过程中可能出现具有不同协方差结构的额外分量，本文以积分平方谱密度为例展示了该现象。
英文摘要：
Integrals of spectral densities are frequently used to summarize spectral characteristics of linear processes. This work studies self-normalization for estimators of such integrals based on sequential periodograms and establishes weak convergence of the corresponding processes. For linear functionals of the spectral density, self-normalization yields pivotal limiting distributions that are free of unknown spectral quantities. For non-linear functionals, however, additional components with distinct covariance structures may arise in the limiting process. We demonstrate this phenomenon for the integrated squared spectral density.
