Uniform Convergence of Multivariate Spectral Density Estimates

2015/05/14 by Wei Biao Wu, Wu, Wei Biao, Paolo Zaffaroni +1 · 1 citation
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference #stat.ME

paper · pdf · doi:10.48550/arxiv.1505.03659

arxiv created 2015/05/14 · openalex publication_date 2015/05/14 · arxiv updated 2015/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory complements earlier results which primarily concern weak or in-probability convergence.

Cited by

• Large Spectral Density Matrix Estimation by Thresholding

Related

• Gaussian Approximation for Lag-Window Estimators and the Construction of Confidence bands for the Spectral Density
• Empirical spectral processes for stationary state space models
• Multivariate Spectral Estimation based on the concept of Optimal Prediction
• Estimating a multivariate Lévy density based on discrete observations
• On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators