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.
Keywords
Nonparametric regression Nadaraya-Watson kernel estimator Adaptive kernel estimation Kernel density estimation
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- Sain, S. R. Adaptive Kernel Density Estimation (Unpublished Ph.D. Thesis, Department of Statistics, Rice University, 1994).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.
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- Sain, S. R. Adaptive Kernel Density Estimation (Unpublished Ph.D. Thesis, Department of Statistics, Rice University, 1994).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.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | March 1, 2010 |
| Published in Issue | Year 2010 Volume: 39 Issue: 3 |