Large Deviations for random power moment problem

• Fabrice Gamboa ^[1] ; Li-Vang Lozada-Chang ^[2]
  1. [1] Paul Sabatier University

     Paul Sabatier University

     Arrondissement de Toulouse, Francia

     
  2. [2] Universidad de La Habana

     Universidad de La Habana

     Cuba

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 3, 2, 2004, págs. 2819-2837
• Idioma: inglés
• DOI: 10.1214/009117904000000559
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider the set Mn of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in Mn, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by Chang, Kemperman and Studden [Ann. Probab. 21 (1993) 1295–1309]. Surprisingly, our large deviations results allow us to compute explicitly the (n+1)th moment range size of the set of all probability measures having the same n first moments. The main tool to obtain these results is the representation of Mn on canonical moments [see the book of Dette and Studden].