Properties of spatial cross-periodograms using fixed-domain asymptotics

Chae Young Lim and Michael Stein

Journal of Multivariate Analysis, 2008, vol. 99, issue 9, 1962-1984

Abstract: Cross-periodograms can be used to study a multivariate spatial process observed on a lattice. For spatial data, it is often appropriate to study asymptotic properties of statistical procedures under fixed-domain asymptotics in which the number of observations increases in a fixed region while shrinking distances between neighboring observations. Using fixed-domain asymptotics, we prove relative asymptotic unbiasedness and relative consistency of a smoothed cross-periodogram after appropriate filtering of the data. In addition, we show that smoothed cross-periodograms are asymptotically normal when the process is stationary multivariate Gaussian with appropriate assumptions on high-frequency behavior of the spectral density.

Keywords: 60G15; 62M15; 62M30; Multivariate; Gaussian; process; Infill; asymptotics; Spectral; density; Fourier; transform; Joint; cumulant (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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