Trimmed regions induced by parameters of a probability

  • Authors:

  • Ignacio Cascos;Miguel López-Díaz

  • Affiliations:

  • Department of Statistics, Universidad Carlos III de Madrid, Av. Universidad 30, E-28911 Leganés, Madrid, Spain;Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, c/ Calvo Sotelo s/n, E-33007 Oviedo, Spain

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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Abstract

Consider any kind of parameter for a probability distribution and a fixed distribution. We study the subsets of the parameter space constituted by all the parameters of the probabilities in the @a-trimming of the fixed distribution. These sets will be referred to as parameter trimmed regions. They are composed of all parameter candidates whose degree of suitability as such a parameter for the distribution is, at least, a specific value @a. In particular, we analyze location, scale, and location-scale parameters and study the properties of the trimmed regions induced by them. Several specific examples of parameter trimmed regions are studied. Among them, we should mention the zonoid trimmed regions obtained when the chosen parameter is the mean value and the location-scale regions of a univariate distribution obtained when the parameter is the pair given by the mean and the standard deviation.