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ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS

Year 2010, Volume: 39 Issue: 3, 429 - 437, 01.03.2010

Abstract

Nonparametric kernel estimators are widely used in many research areas of statistics. An important nonparametric kernel estimator of a regression function is the Nadaraya-Watson kernel regression estimator which is often obtained by using a fixed bandwidth. However, the adaptive kernel estimators with varying bandwidths are specially used to estimate density of the long-tailed and multi-mod distributions. In this paper, we consider the adaptive Nadaraya-Watson kernel regression estimators. The results of the simulation study show that the adaptive
Nadaraya-Watson kernel estimators have better performance than the kernel estimations with fixed bandwidth.

References

  • Abramson, I. On bandwidth variation in kernel estimates - a square-root law, Ann. Statist. 10, 1217–1223, 1982.
  • Hardle, W. Applied Nonparametric Regression (Cambridge, New Rochelle, 1990).
  • Hardle, W. Smoothing Techniques. With Implementation in S. (Springer-Verlag, New York, 1991).
  • Nadaraya, E. A. On nonparametric estimates of density functions and regression curves, Theory Appl. Probability 10, 186–190, 1965.
  • Pagan, A. and Ullah, A. Nonparametric Econometrics (Cambridge University Press, Cam- bridge, 1999).
  • Sain, S. R. Adaptive Kernel Density Estimation (Unpublished Ph.D. Thesis, Department of Statistics, Rice University, 1994).
  • Silverman, B. W. Density Estimation for Statistics and Data Analysis (Chapman & Hall, New York, 1986).
  • Watson, G. S. Smooth regression analysis, Sankhya 26 (15), 175–184, 1964.

ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS

Year 2010, Volume: 39 Issue: 3, 429 - 437, 01.03.2010

Abstract

References

  • Abramson, I. On bandwidth variation in kernel estimates - a square-root law, Ann. Statist. 10, 1217–1223, 1982.
  • Hardle, W. Applied Nonparametric Regression (Cambridge, New Rochelle, 1990).
  • Hardle, W. Smoothing Techniques. With Implementation in S. (Springer-Verlag, New York, 1991).
  • Nadaraya, E. A. On nonparametric estimates of density functions and regression curves, Theory Appl. Probability 10, 186–190, 1965.
  • Pagan, A. and Ullah, A. Nonparametric Econometrics (Cambridge University Press, Cam- bridge, 1999).
  • Sain, S. R. Adaptive Kernel Density Estimation (Unpublished Ph.D. Thesis, Department of Statistics, Rice University, 1994).
  • Silverman, B. W. Density Estimation for Statistics and Data Analysis (Chapman & Hall, New York, 1986).
  • Watson, G. S. Smooth regression analysis, Sankhya 26 (15), 175–184, 1964.
There are 8 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

S. Demir

Ö. Toktamiş This is me

Publication Date March 1, 2010
Published in Issue Year 2010 Volume: 39 Issue: 3

Cite

APA Demir, S., & Toktamiş, Ö. (2010). ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS. Hacettepe Journal of Mathematics and Statistics, 39(3), 429-437.
AMA Demir S, Toktamiş Ö. ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS. Hacettepe Journal of Mathematics and Statistics. March 2010;39(3):429-437.
Chicago Demir, S., and Ö. Toktamiş. “ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS”. Hacettepe Journal of Mathematics and Statistics 39, no. 3 (March 2010): 429-37.
EndNote Demir S, Toktamiş Ö (March 1, 2010) ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS. Hacettepe Journal of Mathematics and Statistics 39 3 429–437.
IEEE S. Demir and Ö. Toktamiş, “ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 3, pp. 429–437, 2010.
ISNAD Demir, S. - Toktamiş, Ö. “ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS”. Hacettepe Journal of Mathematics and Statistics 39/3 (March 2010), 429-437.
JAMA Demir S, Toktamiş Ö. ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS. Hacettepe Journal of Mathematics and Statistics. 2010;39:429–437.
MLA Demir, S. and Ö. Toktamiş. “ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 3, 2010, pp. 429-37.
Vancouver Demir S, Toktamiş Ö. ON THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATORS. Hacettepe Journal of Mathematics and Statistics. 2010;39(3):429-37.