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Simple tests for the validity of correlation function models on the circle

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  • Gneiting, Tilmann

Abstract

We present two simple and efficient tests for the positive definiteness of a given function on the circle. The first criterion is an analogue of Pólya's theorem, and the second is a necessary condition in terms of derivatives. Some hints at applications in geostatistics are given as well.

Suggested Citation

  • Gneiting, Tilmann, 1998. "Simple tests for the validity of correlation function models on the circle," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 119-122, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:2:p:119-122
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    References listed on IDEAS

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    1. Wood, Andrew T. A., 1995. "When is a truncated covariance function on the line a covariance function on the circle?," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 157-164, August.
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    Cited by:

    1. Peter F. Craigmile, 2003. "Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 505-511, September.
    2. Huang, Chunfeng & Zhang, Haimeng & Robeson, Scott M., 2016. "Intrinsic random functions and universal kriging on the circle," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 33-39.

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