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2017 An asymptotic theory for spectral analysis of random fields
Soudeep Deb, Mohsen Pourahmadi, Wei Biao Wu
Electron. J. Statist. 11(2): 4297-4322 (2017). DOI: 10.1214/17-EJS1326


For a general class of stationary random fields we study asymptotic properties of the discrete Fourier transform (DFT), periodogram, parametric and nonparametric spectral density estimators under an easily verifiable short-range dependence condition expressed in terms of functional dependence measures. We allow irregularly spaced data which is indexed by a subset $\Gamma $ of $\mathbb{Z}^{d}$. Our asymptotic theory requires minimal restriction on the index set $\Gamma $. Asymptotic normality is derived for kernel spectral density estimators and the Whittle estimator of a parameterized spectral density function. We also develop asymptotic results for a covariance matrix estimate.


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Soudeep Deb. Mohsen Pourahmadi. Wei Biao Wu. "An asymptotic theory for spectral analysis of random fields." Electron. J. Statist. 11 (2) 4297 - 4322, 2017.


Received: 1 March 2017; Published: 2017
First available in Project Euclid: 13 November 2017

zbMATH: 1383.62209
MathSciNet: MR3724221
Digital Object Identifier: 10.1214/17-EJS1326

Keywords: irregular spaced data , Random fields , Spectral density , time series


Vol.11 • No. 2 • 2017
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