Kernel distribution estimation for grouped data

• Miguel Reyes ^[1] ; Mario Francisco-Fernández ^[2] ; Ricardo Cao ^[2] ; Daniel Barreiro-Ures ^[2]
  1. [1] Universidad de las Américas Puebla

     Universidad de las Américas Puebla

     México

     
  2. [2] Universidade da Coruña

     Universidade da Coruña

     A Coruña, España

     
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 43, Nº. 2, 2019, págs. 259-288
• Idioma: inglés
• Enlaces
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• Resumen

  • Interval-grouped data appear when the observations are not obtained in continuous time, but monitored in periodical time instants. In this framework, a nonparametric kernel distribution estimator is proposed and studied. The asymptotic bias, variance and mean integrated squared error of the new approach are derived. From the asymptotic mean integrated squared error, a plug-in bandwidth is proposed. Additionally, a bootstrap selector to be used in this context is designed. Through a comprehensive simulation study, the behaviour of the estimator and the bandwidth selectors considering different scenarios of data grouping is shown. The performance of the different approaches is also illustrated with a real grouped emergence data set of Avena sterilis (wild oat).