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Fourier analysis of irregularly spaced data on R d
Author(s) -
Matsuda Yasumasa,
Yajima Yoshihiro
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00685.x
Subject(s) - estimator , frequency domain , parametric statistics , series (stratigraphy) , fourier series , mathematics , spectral density , fourier transform , spectral density estimation , domain (mathematical analysis) , periodogram , parametric model , algorithm , mathematical analysis , statistics , geology , paleontology
Summary. 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.