Fourier analysis of irregularly spaced data on Rd

• 成果类型: Article
• 署名作者: Matsuda, Yasumasa; Yajima, Yoshihiro
• 署名单位: Tohoku University; University of Tokyo
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00685.x
• 发表日期: 2009
• 页码: 191-217
• 关键词: parameter-estimation; Cross-validation; stationary

摘要

The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on R-d. We extend the original definition of a periodogram for time series to that for irregularly spaced data and define non-parametric and parametric spectral density estimators in a way that is similar to the classical approach. Introduction of the mixed asymptotics, which are one of the asymptotics for irregularly spaced data, makes it possible to provide asymptotic theories to the spectral estimators. The asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data. Empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches.