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Tube formula for spherically contoured random fields with subexponential marginals

Author

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  • Kuriki, Satoshi
  • Spodarev, Evgeny

Abstract

It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value c. The relative approximation error Δ(c) is exponentially small as a function of c when c tends to infinity. On the other hand, little is known about non-Gaussian random fields.

Suggested Citation

  • Kuriki, Satoshi & Spodarev, Evgeny, 2026. "Tube formula for spherically contoured random fields with subexponential marginals," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:spapps:v:195:y:2026:i:c:s0304414925003023
    DOI: 10.1016/j.spa.2025.104858
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    2. Lu, Xiaolei & Kuriki, Satoshi, 2017. "Simultaneous confidence bands for contrasts between several nonlinear regression curves," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 83-104.
    3. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    Full references (including those not matched with items on IDEAS)

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