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A note on the higher moments of the Euler characteristic of the excursion sets of random fields

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  • Taheriyoun, Ali Reza
  • Shafie, Khalil
  • Jozani, Mohammad Jafari

Abstract

In this paper, a useful and suitable form of the second moment of the Euler characteristic (EC) of excursion sets of a random field with respect to a special threshold is presented, which can be used in numerical evaluations of the variance of EC. We also present an extension to the higher moments of EC. Finally, a new method of simulating is presented and the results are compared with the three older well known methods of simulation based on the moment estimation and monte carlo idea.

Suggested Citation

  • Taheriyoun, Ali Reza & Shafie, Khalil & Jozani, Mohammad Jafari, 2009. "A note on the higher moments of the Euler characteristic of the excursion sets of random fields," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1074-1082, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:8:p:1074-1082
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    Cited by:

    1. Taheriyoun, Ali Reza, 2012. "Testing the covariance function of stationary Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 606-613.
    2. Estrade, Anne & Fournier, Julie, 2016. "Number of critical points of a Gaussian random field: Condition for a finite variance," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 94-99.

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