A collocation method for the sequential testing of a gamma process

Bruno Buonaguidi, B. Buonaguidi, P. Muliere

Risultato della ricerca: Contributo in rivistaArticolo in rivista

2 Citazioni (Scopus)

Abstract

We study the Bayesian problem of sequential testing of two simple hypotheses about the parameter α > 0 of a Lévy gamma process. The initial optimal stopping problem is reduced to a free-boundary problem where, at the unknown boundary points separating the stopping and continuation set, the principles of the smooth and/or continuous fit hold and the unknown value function satisfies on the continuation set a linear integro-differential equation. Due to the form of the Lévy measure of a gamma process, determining the solution of this equation and the boundaries is not an easy task. Hence, instead of solving the problem analytically, we use a collocation technique: the value function is replaced by a truncated series of polynomials with unknown coefficients that, together with the boundary points, are determined by forcing the series to satisfy the boundary conditions and, at fixed points, the integro-differential equation. The proposed numerical technique is employed in well-understood problems to assess its efficiency.
Lingua originaleEnglish
pagine (da-a)1527-1546
Numero di pagine20
RivistaStatistica Sinica
Volume25
DOI
Stato di pubblicazionePubblicato - 2015

Keywords

  • Bayes decision rule
  • Chebyshev polynomials
  • Collocation method
  • Free-boundary problem
  • Gamma process
  • Optimal stopping
  • Sequential testing
  • Smooth and continuous fit principles
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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