Fourier analysis of irregularly spaced data on Rd

Yasumasa Matsuda, Yoshihiro Yajima

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on Rd. 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.

Original languageEnglish
Pages (from-to)191-217
Number of pages27
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
Publication statusPublished - 2009 Jan 1


  • Aliasing
  • Fourier transform
  • Irregularly spaced data
  • Mixed asymptotics
  • Periodogram
  • Spectral density function
  • Taper
  • Whittle likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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