## Electronic Journal of Statistics

### An asymptotic theory for spectral analysis of random fields

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 4297-4322.

Dates
First available in Project Euclid: 13 November 2017

https://projecteuclid.org/euclid.ejs/1510563632

Digital Object Identifier
doi:10.1214/17-EJS1326

Mathematical Reviews number (MathSciNet)
MR3724221

Zentralblatt MATH identifier
1383.62209

#### Citation

Deb, Soudeep; Pourahmadi, Mohsen; Wu, Wei Biao. An asymptotic theory for spectral analysis of random fields. Electron. J. Statist. 11 (2017), no. 2, 4297--4322. doi:10.1214/17-EJS1326. https://projecteuclid.org/euclid.ejs/1510563632

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