Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation

Gérard Collomb; Pascal Sarda; Philippe Vieu

Commentationes Mathematicae Universitatis Carolinae (1985)

  • Volume: 026, Issue: 4, page 789-798
  • ISSN: 0010-2628

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Collomb, Gérard, Sarda, Pascal, and Vieu, Philippe. "Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation." Commentationes Mathematicae Universitatis Carolinae 026.4 (1985): 789-798. <http://eudml.org/doc/17426>.

@article{Collomb1985,
author = {Collomb, Gérard, Sarda, Pascal, Vieu, Philippe},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {kernel estimate; bandwidth choice; convergence in probability; weak pointwise consistency; cross-validatory window estimate},
language = {eng},
number = {4},
pages = {789-798},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation},
url = {http://eudml.org/doc/17426},
volume = {026},
year = {1985},
}

TY - JOUR
AU - Collomb, Gérard
AU - Sarda, Pascal
AU - Vieu, Philippe
TI - Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1985
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 026
IS - 4
SP - 789
EP - 798
LA - eng
KW - kernel estimate; bandwidth choice; convergence in probability; weak pointwise consistency; cross-validatory window estimate
UR - http://eudml.org/doc/17426
ER -

References

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  1. COLLOMB G., Estimation non paramétrique de la régression par la méthode du noyau, Thèse, Université Paul Sabatier, Toulouse, 1976. (1976) 
  2. COLLOMB G., Quelques propriétés de la méthode du noyau pour l'estimation non paramétrique de la régression en un point fixé, Comptes Rendus à l'Académie des Sciences de Paris 285, Série A, 1977, 289-292. (1977) Zbl0375.62042MR0474612
  3. COLLOMB G., Conditions nécessaires et suffisantes de convergence uniforme d'un estimateur de la régression, estimation des dérivées de la régression, Comptes Rendus à l'Académie des Sciences de Paris 288, Série A, 1978, 161-164. (1978) MR0524775
  4. COLLOMB G., Estimation de la régression par la méthode des k points les plus proches avec noyau: quelques propriétés de convergence ponctuelle, Lectures Notes in Mathematics 821, 1979, 159-175. (1979) MR0604024
  5. COLLOMB G., Estimation non paramétrique de la régression: revue bibliographique, International Statistical Review 49, 1981, 75-93. (1981) Zbl0471.62039MR0623011
  6. COLLOMB G., Non parametric regression: an up-to-date bibliography, Mathematlsche Operationsforschung und Statistik, Ser. Statistics, to appear, 1985. (1985) 
  7. DEVROYE L., PENROD C. S., The consistency of automatic kernel density estimates, Annals of Statistics 12, 4, 1984, 1231-1249. (1984) Zbl0569.62032MR0760685
  8. HALL P., Asymptotic properties of integrated square error and cross-validation for kernel estimation of a regression function, Zeitschrift für Wahrscheinlichkeitsthéorie u. verw. Gebiete 67, 1984, 175-196. (1984) Zbl0556.62020MR0758072
  9. HÄRDLE W., MARROH J. S., Optimal bandwidth selection in non parametric regression function estimation, preprint, Universität Heidelberg, 1984. (1984) 
  10. NADARAYA E. A., On estimating regression, Theory of Probability and its applications 9, 1964, 141-142. (1964) Zbl0136.40902
  11. RICE J., Bandwidth choice for nonparametric regression, Annals of Statistics 12, 4, 1984, 1215-1230. (1984) Zbl0554.62035MR0760684
  12. ROSENBLATT M., Remarks on some nonparametric estimates of a density function, Annals of Mathematical Statistics 27, 1956, 642-669. (1956) Zbl0073.14602MR0079873
  13. WATSON G. S., Smooth regression analysis, Sankhya, Ser. A, vol. 26, 1964, 359-372. (1964) Zbl0137.13002MR0185765
  14. WONG W. W., On the consistency of cross validation in kernel nonparametric regression, Annals of Statistics 11, 4, 1983, 1136-1141. (1983) Zbl0539.62046MR0720259

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