Properties of spatial cross-periodograms using fixed-domain asymptotics |
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Authors: | Chae Young Lim Michael Stein |
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Institution: | a Department of Statistics and Probability, Michigan State University, A413 Wells Hall, East Lansing, MI 48824, United States b Department of Statistics, University of Chicago, 5734 S, University Avenue, Chicago, IL 60637, United States |
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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. |
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Keywords: | 60G15 62M15 62M30 |
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