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Asymptotic normality of the sample mean and covariances of evanescent fields in noise

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  • Kliger, Mark
  • Francos, Joseph M.

Abstract

We consider the asymptotic properties of the sample mean and the sample covariance sequence of a field composed of the sum of a purely indeterministic and evanescent components. The asymptotic normality of the sample mean and sample covariances is established. A Bartlett-type formula for the asymptotic covariance matrix of the sample covariances of this field, is derived.

Suggested Citation

  • Kliger, Mark & Francos, Joseph M., 2007. "Asymptotic normality of the sample mean and covariances of evanescent fields in noise," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1853-1875, November.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:10:p:1853-1875
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    References listed on IDEAS

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    1. Kallianpur, G. & Miamee, A. G. & Niemi, H., 1990. "On the prediction theory of two-parameter stationary random fields," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 120-149, January.
    2. Li, Ta-Hsin & Kedem, Benjamin & Yakowitz, Sid, 1994. "Asymptotic normality of sample autocovariances with an application in frequency estimation," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 329-349, August.
    3. Chiang, Tse-Pei, 1991. "The prediction theory of stationary random fields. III. Fourfold Wold decompositions," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 46-65, April.
    4. Li, Ta-Hsin, 1996. "Bartlett-type formulas for complex multivariate time series of mixed spectra," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 259-268, July.
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