The Comparison of Bandwidth Selection Methods using Kernel Function
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Abstract
This paper presents the bandwidth selection methods for local polynomial regression with Normal, Epanechnikov, and Uniform kernel function. The bandwidth selection methods are proposed by Histogram Bin Width method, Bandwidth for Kernel Density Estimation method, and Bandwidth for Local Linear Regression method to estimate the local polynomial regression estimator. Using Monte Carlo simulations, we compare the Mean Square Error (MSE) of the bandwidth selection methods. For simulation results, it can be seen that the MSE of Bandwidth for Kernel Density Estimation method provides the smallest in all situations. The bandwidth selection methods are applied to the Stock Exchange of Thailand (SET) index. The results show that the MSE of Kernel Density Estimation method with Normal kernel function is the smallest as the simulation study.
Keywords: Bandwidth, Epanechnikov kernel function, Local linear regression, Local polynomial regression
E-mail: kaautcha@kmitl.ac.th
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References
[2] Nadaraya, E.A., 1964. On estimating regression. Theory of Probability and Its Application,9, 141-142.
[3] Watson, G.S., 1964. Smooth regression analysis, Sankhy Series A, 26, 359-372.
[4] Stone, C.G., 1977. Consistent nonparametric regression, The Annals of Statistics, 5, 595-620.
[5] Cleveland, W.S., 1979. Robust locally weight regression and smoothing scatter plots,Journal of American Statistics Association, 74, 829-836.
[6] Müller, H.G., 1987. Weighted local regression and kernel methods for nonparametric curve fitting. Journal of American Statistics Association, 82, 231- 238.
[7] Allen, D.M., 1974. The relationship between variable and data augmentation and a method of prediction, Technometrics, 16, 125-127.
[8] Stone, M., 1974. Cross-validatory choice and assessment of statistical predictions (with discussion), Journal of the Royal Statistical Society. Series B, 36, 111-147.
[9] Wahba, G., 1977. A survey of some smoothing problems and the method of generalized cross-validation for solving them. In: P.R. Krisnaiah, ed. Application of Statistics, North Holland, Amsterdam, pp. 507-523.
[10] Craven, P. and Wahba, G., 1979. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized crossvalidation. Numerische Mathematik, 31, 377-403.
[11] Epanechnikov, V.A., 1969. Non-parametric estimation of a multivariate probability density.Theory of Probability and its Application, 14, 153-358.
[12] Wand, M.P., 1995. Data-based choice of histogram winbidth. The American Statistician, 51,59-64.
[13] Scott, D.W., 1979. On optimal and data-based histogram, Biometrika, 66, 605- 610.
[14] Sheather, S.J. and Jones, M.C., 1991. A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society, Series B, 53, 683-690.
[15] Park, B.U. and Marron, J.S. 1990. Comparison of data-driven bandwidth selectors, Journal of American Statistics Association, 85, 66 - 72.
[16] Ruppert, D., Sheather, S.J. and Wand, M.P., 1995. An effective bandwidth selector for local least squares regression, Journal of American Statistics Association, 90, 1257-1270.