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  • The most important factor in a multivariate kernel density estimation is a~choice of a bandwidth matrix. Because of its role in controlling both the amount and the direction of multivariate smoothing, this choice is a particularly important. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or pre-transformation of the data. General multivariate kernel density derivative estimators has been investigated in paper Chac\'on, Test, p. 375--398, Vol. 19, 2011. The present paper is focused on data-driven selectors of full bandwidth matrices for a density and its gradient. This method is based on an optimally balanced relation between integrated variance and integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. It is also given the relative rate of convergence to compare the method with cross-validation and plug-in methods.
  • The most important factor in a multivariate kernel density estimation is a~choice of a bandwidth matrix. Because of its role in controlling both the amount and the direction of multivariate smoothing, this choice is a particularly important. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or pre-transformation of the data. General multivariate kernel density derivative estimators has been investigated in paper Chac\'on, Test, p. 375--398, Vol. 19, 2011. The present paper is focused on data-driven selectors of full bandwidth matrices for a density and its gradient. This method is based on an optimally balanced relation between integrated variance and integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. It is also given the relative rate of convergence to compare the method with cross-validation and plug-in methods. (en)
Title
  • Full bandwidth matrix selectors for gradient kernel density estimate
  • Full bandwidth matrix selectors for gradient kernel density estimate (en)
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  • Full bandwidth matrix selectors for gradient kernel density estimate
  • Full bandwidth matrix selectors for gradient kernel density estimate (en)
skos:notation
  • RIV/00216224:14310/13:00067353!RIV14-MSM-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I, P(LC06024), S
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 75844
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/13:00067353
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  • asymptotic mean integrated square error; multivariate kernel density; unconstrained bandwidth matrix (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [59F7FE08F4FE]
http://linked.open...i/riv/nazevZdroje
  • Computational Statistics & Data Analysis
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 57
http://linked.open...iv/tvurceVysledku
  • Koláček, Jan
  • Horová, Ivanka
  • Vopatová, Kamila
http://linked.open...ain/vavai/riv/wos
  • 000310403700027
issn
  • 0167-9473
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.csda.2012.07.006
http://localhost/t...ganizacniJednotka
  • 14310
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