Statistical sampling on metric spaces and application to preference estimation

• Pedro García-Segador ^[1]
  1. [1] Instituto Nacional de Estadística y Geografía

     Instituto Nacional de Estadística y Geografía

     México

     
• Localización: BEIO, Boletín de Estadística e Investigación Operativa, ISSN 1889-3805, Vol. 41, Nº. 3, 2025, págs. 38-52
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This work deals with the problem of using statistical sampling on spaces where no algebraic operations are defined in advance. Sometimes, the target variable is not numeric and finding a good representative value of this variable from a sample is not easy. Clearly, this complexity depends on the nature of the problem and the variables involved. We start discussing a general framework to cope with this kind of problems. Within this theory, we propose the use of different estimators and prove their consistency. We also introduce the necessary tools to work with interval estimations. The properties of estimators depend on the metric space. For this reason, we will proceed to study in detail the particular case of metric spaces whose range of values is composed of partially ordered sets. These variables represent the set of preferences of a collection of individuals regarding some topic. We benefit from Order Theory to build well-behaved metrics and provide a fully operational theory to work with partially ordered sets. Finally, to illustrate these results, we study an application of these results for estimating the voting intention for each political party in some election campaigns.

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