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Efficient computation of the cdf of the maximum distance between Brownian bridge and its concave majorant

Filali, Karim; Balabdaoui, Fadoua (2012), Efficient computation of the cdf of the maximum distance between Brownian bridge and its concave majorant, Journal of Statistical Computation and Simulation, 82, 3, p. 405-418. http://dx.doi.org/10.1080/00949655.2010.534481

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1005.1307v1.pdf (383.9Kb)
Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1005.1307
Date
2012
Journal name
Journal of Statistical Computation and Simulation
Volume
82
Number
3
Publisher
Taylor & Francis
Pages
405-418
Publication identifier
http://dx.doi.org/10.1080/00949655.2010.534481
Metadata
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Author(s)
Filali, Karim
Balabdaoui, Fadoua
Abstract (EN)
In this paper, we describe two computational methods for calculating the cumulative distribution function and the upper quantiles of the maximal difference between a Brownian bridge and its concave majorant. The first method has two different variants that are both based on a Monte Carlo approach, whereas the second uses the Gaver–Stehfest (GS) algorithm for the numerical inversion of the Laplace transform. If the former method is straightforward to implement, it is very much outperformed by the GS algorithm, which provides a very accurate approximation of the cumulative distribution as well as its upper quantiles. Our numerical work has a direct application in statistics: the maximal difference between a Brownian bridge and its concave majorant arises in connection with a nonparametric test for monotonicity of a density or regression curve on [0,1]. Our results can be used to construct very accurate rejection region for this test at a given asymptotic level.
Subjects / Keywords
Monte Carlo; Monotonicity; Gaver–Stehfest algorithm; concave majorant; Brownian bridge
JEL
C15 - Statistical Simulation Methods: General

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