Penalized multivariate Whittle likelihood for power spectrum estimation

• 成果类型: Article
• 署名作者: Krafty, Robert T.; Collinge, William O.
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass088
• 发表日期: 2013
• 页码: 447458
• 关键词: automatic estimation; smoothing parameter; time-series; models

摘要

Nonparametric estimation procedures that can flexibly account for varying levels of smoothness among different functional parameters, such as penalized likelihoods, have been developed in a variety of settings. However, geometric constraints on power spectra have limited the development of such methods when estimating the power spectrum of a vector-valued time series. This article introduces a penalized likelihood approach to nonparametric multivariate spectral analysis through the minimization of a penalized Whittle negative loglikelihood. This likelihood is derived from the large-sample distribution of the periodogram and includes a penalty function that forms a measure of regularity on multivariate power spectra. The approach allows for varying levels of smoothness among spectral components while accounting for the positive definiteness of spectral matrices and the Hermitian and periodic structures of power spectra as functions of frequency. The consistency of the proposed estimator is derived and its empirical performance is demonstrated in a simulation study and in an analysis of indoor air quality.