Kernel distribution estimation for grouped data

  1. Miguel Reyes 1
  2. Mario Francisco-Fernández 2
  3. Ricardo Cao 2
  4. Daniel Barreiro-Ures 2
  1. 1 Universidad de las Américas-Puebla, Puebla, México
  2. 2 Universidade da Coruña
    info

    Universidade da Coruña

    La Coruña, España

    ROR https://ror.org/01qckj285

Journal:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Year of publication: 2019

Volume: 43

Issue: 2

Pages: 259-288

Type: Article

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More publications in: Sort: Statistics and Operations Research Transactions

Abstract

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).

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Funding information

This research has been supported by MINECO grants MTM2014-52876-R and MTM2017-82724-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF.

Funders

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