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The Supremum of Chi-Square Processes

Author

Listed:
  • Charles-Elie Rabier

    (Université de Toulouse
    INRA UR631)

  • Alan Genz

    (Washington State University)

Abstract

We describe a lower bound for the critical value of the supremum of a Chi-Square process. This bound can be approximated using an RQMC simulation. We compare numerically this bound with the upper bound given by Davies, only suitable for a regular Chi-Square process. In a second part, we focus on a non regular Chi-Square process: the Ornstein–Uhlenbeck Chi-Square process. Recently, Rabier et al. (2009) have shown that this process has an application in genetics: it is the limiting process of the likelihood ratio test process related to the test of a gene on an interval representing a chromosome. Using results from Delong (Commun Stat Theory Method A10(20):2197–2213, 1981), we propose a theoretical formula for the supremum of such a process and we compare it in particular with our simulated lower bound.

Suggested Citation

  • Charles-Elie Rabier & Alan Genz, 2014. "The Supremum of Chi-Square Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 715-729, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-013-9331-1
    DOI: 10.1007/s11009-013-9331-1
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    Cited by:

    1. Charles-Elie Rabier & Jean-Marc Azaïs & Jean-Michel Elsen & Céline Delmas, 2019. "Chi-square processes for gene mapping in a population with family structure," Statistical Papers, Springer, vol. 60(1), pages 239-271, February.

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