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Kernel distribution estimation for grouped data

    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
  • 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).

  • Referencias bibliográficas
    • Altman, N. and Leger, C. (1995). Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference,...
    • Anastasiou, K., Kechriniotis A. and Kotsos, B. (2006). Generalizations of the Ostrowski’s inequality. Journal of Interdisciplinary Mathematics,...
    • Azzalini, A. (1981). A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika, 68, 326–328.
    • Barreiro, D., Fraguela, B., Doallo, R., Cao, R., Francisco-Fernandez, M. and Reyes, M. (2019). binnednp: Nonparametric estimation for interval-grouped...
    • Blower, G. and Kelsall, J. E. (2002). Nonlinear kernel density estimation for binned data: convergence in entropy. Bernoulli, 8, 423–449.
    • Bowman, A., Hall, P. and Prvan, T. (1998). Bandwidth selection for the smoothing of distribution functions. Biometrika, 85, 799–808.
    • Brown, L., Cai, T., Zhang, R., Zhao, L. and Zhou, H. (2010). The root-unroot algorithm for density estimation as implemented via waved block...
    • Cao, R., Francisco-Fernández, M., Anand, A., Bastida, F. and González-Andújar, J. L. (2011). Computing statistical indices for hydrothermal...
    • Cao, R., Francisco-Fernández, M., Anand, A., Bastida, F. and González-Andújar, J. L. (2013). Modeling Bromus diandrus seedling emergence...
    • Coit, D. and Dey, K. (1999). Analysis of grouped data from field-failure reporting systems. Reliability Engineering & System Safety, 65,...
    • Dutta, S. (2015). Local smoothing for kernel distribution function estimation. Communications in Statistics, Simulation and Computation, 44,...
    • González-Andújar, J. L., Francisco-Fernández, M., Cao, R., Reyes, M., Urbano, J. M., Forcella, F. and Bastida, F. (2016). A comparative...
    • Guo, S. (2005). Analysing grouped data with hierarchical linear modeling. Children and Youth Services Review, 27, 637–652.
    • Hill, P. (1985). Kernel estimation of a distribution function. Communications in Statistics, Theory and Methods, 14, 605–620.
    • Klein, J. P. and Moeschberger, M. (1997). Survival Analysis. New York: Springer Verlag.
    • Mächler, M. (2017). nor1mix: Normal (1-d) Mixture Models (S3 Classes and Methods). https://CRAN. R-project.org/package=nor1mix. R package...
    • Mack, Y. (1984). Remarks on some smoothed empirical distribution functions and processes. Bulletin of Informatics and Cybernetics, 21, 29–35.
    • Mclachlan, G. and Peel, D. (2000). Finite Mixture Models. New York: John Wiley & Sons, Inc.
    • Minoiu, C. and Reddy, S. (2009). Estimating poverty and inequality from grouped data: How well do parametric methods perform? Journal of Income...
    • Nadaraya, E. (1964). On estimating regression. Theory of Probability and Applications, 10, 186–190.
    • Ostrowski, A. (1938). Über die Absolutabweichung einer differenzierbaren Funktion von ihrem Integralmittelwert. Commentarii Mathematici...
    • Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33, 1065–1076.
    • Pipper, C. and Ritz, C. (2007). Checking the grouped data version of the Cox model for interval-grouped data survival data. Scandinavian Journal...
    • Polanski, A. and Baker, E. (2000). Multistage plug-in bandwidth selection for kernel distribution function estimates. Journal of Statistical...
    • Quintela-del-Rı́o, A. and Estévez-Pérez, G. (2012). Nonparametric kernel distribution function estimation with kerdiest: An R package...
    • R Core Team (2019). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
    • Reiss, R. (1981). Nonparametric estimation of smooth distribution functions. Scandinavian Journal of Statistics, 8, 116–119.
    • Reyes, M., Francisco-Fernandez, M. and Cao, R. (2016). Nonparametric kernel density estimation for general grouped data. Journal of Nonparametric...
    • Reyes, M., Francisco-Fernández, M. and Cao, R. (2017). Bandwidth selection in kernel density estimation for interval-grouped data. TEST,...
    • Rizzi, S., Thinggaard, M., Engholm, G., Christensen, N., Johannesen, T., Vaupel, J. and Jacobsen, R. (2016). Comparison of non-parametric...
    • Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27, 832–837.
    • Sarda, P. (1993). Smoothing parameter selection for smooth distribution function. Journal of Statistical Planning and Inference, 35, 65–75.
    • Scott, D. and Sheather, S. (1985). Kernel density estimation with binned data. Communications in Statistics, Theory and Methods, 27, 832–837.
    • Titterington, D. (1983). Kernel-based density estimation using censored, truncated or grouped data. Communications in Statistics, Theory and...
    • Turnbull, B. W. (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical...
    • Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. London: Chapman and Hall/CRC.
    • Wang, B. and Wang, X.-F. (2016). Fitting the generalized lambda distribution to pre-binned data. Journal of Statistical Computation and Simulation,...
    • Wang, B. and Wertelecki, W. (2013). Density estimation for data with rounding errors. Computational Statistics & Data Analysis, 65, 4–12.

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