Remarks on optimum kernels and optimum boundary kernels

Jitka Poměnková

Applications of Mathematics (2008)

  • Volume: 53, Issue: 4, page 305-317
  • ISSN: 0862-7940

Abstract

top
Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.

How to cite

top

Poměnková, Jitka. "Remarks on optimum kernels and optimum boundary kernels." Applications of Mathematics 53.4 (2008): 305-317. <http://eudml.org/doc/37786>.

@article{Poměnková2008,
abstract = {Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.},
author = {Poměnková, Jitka},
journal = {Applications of Mathematics},
keywords = {kernel; optimum kernel; optimum boundary kernel},
language = {eng},
number = {4},
pages = {305-317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on optimum kernels and optimum boundary kernels},
url = {http://eudml.org/doc/37786},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Poměnková, Jitka
TI - Remarks on optimum kernels and optimum boundary kernels
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 305
EP - 317
AB - Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.
LA - eng
KW - kernel; optimum kernel; optimum boundary kernel
UR - http://eudml.org/doc/37786
ER -

References

top
  1. Gasser, T. L., Müller, H.-G., Mammitzsch, V., Kernels for nonparametric curve estimation, J. R. Stat. Soc. B47 (1985), 238-251. (1985) MR0816088
  2. Granovsky, B. L., Müller, H.-G., 10.2307/1403693, Int. Stat. Rev. 59 (1991), 373-388. (1991) DOI10.2307/1403693
  3. Granovsky, B. L., Müller, H.-G., Pfeifer, C., Some remarks on optimal kernel function, Stat. Decis. 13 (1995), 101-116. (1995) MR1342732
  4. Härdle, W., Applied Nonparametric Regression, Cambridge University Press Cambridge (1990). (1990) MR1161622
  5. Horová, I., Gegenbauer polynomials, optimal kernels and Stancu operators, Approximation Theory and Function Series Budapest (Hungary), 1995 P. Vértesi et al. János Bolyai Mathematical Socity Budapest (1996), 227-235. (1996) MR1432671
  6. Horová, I., Some remarks on kernels, J. Comput. Anal. Appl. 2 (2000), 253-263. (2000) MR1778550
  7. Horová, I., Optimization problems connected with kernel estimates, Signal Processing, Communications and Computer Science World Scientific and Engineering Society Press (2002), 339-334. (2002) 
  8. Kolaček, J., Poměnková, J., Comparative study of boundary effects for kernel smoothing, Austr. J. Stat. 35 (2006), 281-288. (2006) 
  9. Mammitzsch, V., The fluctuation of kernel estimators under certain moment conditions, Proc. ISI 1985 (1985), 17-18. (1985) 
  10. Poměnková, J., Gasser-Müller's estimate, LI, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 3 (2004), Czech. (2004) MR2159138
  11. Poměnková, J., Some aspects of smoothing the regression function, PhD. thesis University of Ostrava Ostrava (2005), Czech. (2005) 
  12. Poměnková, J., Optimal kernels, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, LII (2004), 69-77 Czech. (2004) 
  13. Poměnková, J., Optimum choice of the bandwidth using AMSE for the Gasser-Müller estimator, Applications of Mathematics and Statistics in Economy University of Economics and Faculty of Informatics and Statistics Praha (2004), 192-198. (2004) 
  14. Szegö, G., Orthogonal Polynomials. American Mathematical Society Colloquium Publications, Vol. 23, Am. Math. Soc. New York (1939). (1939) 
  15. Wand, M. P., Jones, M. C., Kernel Smoothing, Chapman &amp; Hall London (1995). (1995) Zbl0854.62043MR1319818

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.