Choice of Bandwidth for Nonparametric Regression Models using Kernel Smoothing: A Simulation Study


Abstract


In this study, kernel smoothing method is considered in the estimation of nonparametric regression models. A crucial step in the implementation of this method is to select a proper bandwidth (smoothing parameter). In an attempt to address the specification of amount of smoothing, this article provides a comparative study of different methods (or criteria) for choosing the smoothing parameter. Given the need of automatic data-driven smoothing parameter selectors for applied statistics, this study is focused to explain and compare these methods. In this context, we generalized the selection methods used in the smoothing spline method for kernel smoothing. In order to explore and compare the performance of these methods, a simulation study is performed for data sets with different sample sizes. As a result of simulation, the appropriate selection criteria are provided for a suitable smoothing parameter selection.


Keywords


Kernel smoothing; Smoothing spline; Nonparametric regression; Bandwidth; Selection method.

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References


P. Craven, and G. Wahba. Smoothing Noisy Data With Spline Functions. Numerische Mathematik, vol.31, pp.377403, 1979.

E. Heckman. Spline Smoothing in a Partly Linear Model, Journal of the Royal Statistical Society. Series B (Methodological), vol.48, pp. 244-248, 1986.

W. Hardle. Applied Nonparametric Regression. Cambridge University Press, Cambridge, 1991.

W. Hardle, P. Hall, and J.S. Marron. How Far are Automatically Chosen Regression Smoothing Parameters From Their Optimum? (With Discussion). Journal of the American Statistical Association, vol. 83, pp.8689, 1988.

G. Wahba. Spline models for observation data. SIAM, Pennslylvania, 1990.

T. Hastie, and R. Tibshirani. Genaralized Additive Models. Chapman & Hall, London, 1990.

C.M. Hurvich, J.S. Simonoff, and C.L., Tsai. Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. Journal of the Royal Statistical Society. Series B (Methodological), vol. 60, pp.271-293, 1998.

R.L. Eubank. Nonparametric Regression and Spline Smoothing. New York, 1999.

T.C.M. Lee, and V.Solo. Bandwidth Selection for Local Linear Regression: A Simulation Study. Computational Statistics, vol. 14, pp. 515532, 1999.

M.G. Schimek. Estimation and Inference in Partially Linear Models with Smoothing Splines. Journal of Statistical Planning and Inference, vol. 91, pp. 525-540, 2000.

E. Cantoni, and E. Ronchetti. Resistant Selection of Smoothing Parameter for Smoothing Splines. Statisics and Computing, vol.11, pp.141146, 2001.

T.C.M. Lee. A Stabilized Bandwidth Selection Method for Kernel Smoothing of Periodiagram. Signal Process, vol. 81, pp.419-430, 2001.

S.C. Kou, and B. Efron. Smoothers and the Cp, generalized maximum likelihood, and extended exponential criteria. Jasa, vol. 97, pp. 766-782, 2002.

D. Ruppert, M. P. Wand, and R. J. Carroll. Semiparametric Regression. Cambridge University Press, Cambridge, 2003.

T.C.M. Lee. Smoothing parameter selection for smoothing splines: a simulation study. Computational Statistics & Data Analysis,vol. 42, pp.139-148, 2003.

D. Ayd?n. A Comparison of the Nonparametric Regression Models Using Smoothing Spline and Kernel Regression. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, vol .1, pp. 588-592, 2007.

T. Krivobokova, and G. Kauermann. A note on penalized spline smoothing with correlated errors. Journal of the American Statistical Association, vol, 102, pp. 1328-1337, 2007.

D. Ayd?n, and M. Memmedli. Optimum Smoothing Parameter Selection for Penalized Least Squares in Form of Linear Mixed Effect Models. Optimization: A Journal of Mathematical Programming and Operations Research, vol. 61(4), pp. 459-476, 2012.

C. Loader. Smoothing: Local Regression Techniques. Papers / Humboldt-Universitt Berlin, Center for Applied Statistics and Economics (CASE), No.12, 2004.

W. Hardle, M. Muller, S. Sperlich, and A. Werwatz. Nonparametric and Semiparametric Models, Springer, New York, 305, 2004.

C.L. Mallows. Some comments on CP. Technometrics, vol.15, pp. 661-675, 1973.

P.T. Reis, and R.T. Ogden. Smoothing Parameter Selection for A Class of Semiparametric Linear Models. Journal of the Royal Statistical Society. Series B (Methodological), vol.71, pp. 505523, 2009.

SPSS. SPSS for Windows. Version 16.0, Chicago, SPSS Inc.,USA, 2010.


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