Bounds and asymptotic expansions for the distribution of the maximum of a smooth stationary gaussian process

 Access to full text

 Full (PDF)

1. [1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dover, New York ( 1972). Zbl0543.33001MR208797
2. [2] R.J. Adler, An Introduction to Continuity, Extrema and Related Topics for General Gaussian Processes, IMS, Hayward, Ca ( 1990). Zbl0747.60039MR1088478
3. [3] J.-M. Azaïs and M. Wschebor, Une formule pour calculer la distribution du maximum d'un processus stochastique. C.R. Acad. Sci. Paris Ser. I Math. 324 ( 1997) 225-230. Zbl0880.60056MR1438389
4. [4] J-M. Azaïs and M. Wschebor, The Distribution of the Maximum of a Stochastic Process and the Rice Method, submitted. Zbl1018.60036
5. [5] C. Cierco, Problèmes statistiques liés à la détection et à la localisation d'un gène à effet quantitatif. PHD dissertation. University of Toulouse, France ( 1996). 
6. [6] C. Cierco and J.-M. Azaïs, Testing for Quantitative Gene Detection in Dense Map, submitted. 
7. [7] H. Cramér and M.R. Leadbetter, Stationary and Related Stochastic Processes, J. Wiley & Sons, New-York ( 1967). Zbl0162.21102MR217860
8. [8] D. Dacunha-Castelle and E. Gassiat, Testing in locally conic models, and application to mixture models. ESAIM: Probab. Statist. 1 ( 1997) 285-317. Zbl1007.62507MR1468112
9. [9] R.B. Davies, Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64 ( 1977) 247-254. Zbl0362.62026MR501523
10. [10] J. Ghosh and P. Sen, On the asymptotic performance of the log-likelihood ratio statistic for the mixture model and related results, in Proc. of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, Le Cam L.M. and Olshen R.A., Eds. ( 1985). MR822065
11. [11] M.F. Kratz and H. Rootzén, On the rate of convergence for extreme of mean square differentiable stationary normal processes. J. Appl. Prob. 34 ( 1997) 908-923. Zbl0903.60043MR1484024
12. [12] M.R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New-York ( 1983). Zbl0518.60021MR691492
13. [13] R.N. Miroshin, Rice series in the theory of random functions. Vestnik Leningrad Univ. Math. 1 ( 1974) 143-155. 
14. [14] M.B. Monagan, et al., Maple V Programming guide. Springer ( 1998). Zbl0877.68070
15. [15] V.I. Piterbarg, Comparison of distribution functions of maxima of Gaussian processes. Theory Probab. Appl. 26 ( 1981) 687-705. Zbl0488.60051MR636766
16. [16] V.I. Piterbarg, Large deviations of random processes close to gaussian ones. Theory Probab. Appl. 27 ( 1982) 504-524. Zbl0517.60029MR673920
17. [17] V.I. Piterbarg, Asymptotic Methods in the Theory of Gaussian Processes and Fields. American Mathematical Society. Providence, Rhode Island ( 1996). Zbl0841.60024MR1361884
18. [18] S.O. Rice, Mathematical Analysis of Random Noise. Bell System Tech. J. 23 ( 1944) 282-332; 24 ( 1945) 45-156. Zbl0063.06485MR10932
19. [19] SPLUS, Statistical Sciences, S-Plus Programmer's Manual, Version 3.2, Seattle: StatSci, a division of MathSoft, Inc. ( 1993). 
20. [20] J. Sun, Significance levels in exploratory projection pursuit. Biometrika 78 ( 1991759-769. Zbl0753.62067MR1147012
21. [21] M. Wschebor, Surfaces aléatoires. Mesure géometrique des ensembles de niveau. Springer-Verlag, New-York, Lecture Notes in Mathematics 1147 ( 1985). Zbl0573.60017MR871689

1. Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor, On the tails of the distribution of the maximum of a smooth stationary gaussian process
2. Jean-Marc Azaïs, Christine Cierco-Ayrolles, An asymptotic test for quantitative gene detection
3. Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor, On the tails of the distribution of the maximum of a smooth stationary Gaussian process