A Comparison Between New Modification of Adaptive Nadaraya-Watson Kernel and Classical Adaptive Nadaraya-Watson Kernel Methods in Nonparametric Regression
A Simulation Study
Abstract
Nonparametric kernel estimators are mostly used in a variety of statistical research fields. Nadaraya-Watson kernel estimator (NWK) is one of the most important nonparametric kernel estimator that is often used in regression models with a fixed bandwidth. In this article, we consider the four new Proposed Adaptive Nadaraya-Watson Kernel Regression Estimators (Interquartile Range, Standard Deviation, Mean Absolute Devotion, and Median Absolute Deviation) rather than (Fixed Bandwidth, Adaptive Geometric, Adaptive Mean, Adaptive Range, and Adaptive Median). The outcomes in both simulation and actual data in Leukemia Cancer show that the four new ANW Kernel Estimators (Interquartile Range, Standard Deviation, Mean Absolute devotion, and Median Absolute Deviation) is more effective than the kernel estimations with fixed bandwidth in previous studies using Mean Square Error (MSE) Criterion.
Downloads
References
A. Christmann and I. Steinwart, “Consistency and robustness of kernel-based regression in convex risk minimization,” Bernoulli, vol. 13, no. 3, pp. 799–819, Aug. 2007, doi: 10.3150/07-bej5102.
B. W. Silverman, Density estimation for statistics and data analysis estimation Density. London: Kluwer Academic Publishers, 1986.
D. Conn and G. Li, “An oracle property of the Nadaraya–Watson kernel estimator for high‐dimensional nonparametric regression,” Scandinavian Journal of Statistics, vol. 46, no. 3, pp. 735–764, Dec. 2018, doi: 10.1111/sjos.12370.
D. Li and R. Li, “Local composite quantile regression smoothing for Harris recurrent Markov processes,” Journal of Econometrics, vol. 194, no. 1, pp. 44–56, Sep. 2016, doi: 10.1016/j.jeconom.2016.04.002.
E. A. Nadaraya, “On Estimating Regression,” Theory of Probability & Its Applications, vol. 9, no. 1, pp. 141–142, Jan. 1964, doi: 10.1137/1109020.
G. S. Watson, “Smooth Regression Analysis. Sankhya, Series”, 1964.
H. A. Khulood and I. A. turk Lutfiah, “Modification of the adaptive Nadaraya-Watson kernel regression estimator,” Scientific Research and Essays, vol. 9, no. 22, pp. 966–971, Nov. 2014, doi: 10.5897/sre2014.6121.
H. Takeda, S. Farsiu, and P. Milanfar, “Kernel Regression for Image Processing and Reconstruction,” IEEE Transactions on Image Processing, vol. 16, no. 2, pp. 349–366, Feb. 2007, doi: 10.1109/tip.2006.888330.
M. HANIF, S. SHAHZADI, U. SHAHZAD, and N. KOYUNCU, “On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size,” Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, p. 511, Jun. 2018, doi: 10.19113/sdufbed.70996.
M. Hollander, D. A. Wolfe, and E. Chicken, Nonparametric statistical methods. Hoboken, New Jersey: John Wiley & Sons, Inc, 2014.
M. Memmedli and M. Yildiz, “Comparison study on smoothing parameter and sample size in nonparametric fuzzy local polynomial regression models,” 2012 IV International Conference “Problems of Cybernetics and Informatics” (PCI), Sep. 2012, doi: 10.1109/icpci.2012.6486400.
M. P. Wand and M. C. Jones, Kernel Smoothing. Boston, Ma Springer Us, 1995.
MartínezW. L. and MartínezA. R., Computational Statistics Handbook with MATLAB. London: Chapman & Hall, 2008.
I. S. Abramson, “On Bandwidth Variation in Kernel Estimates-A Square Root Law,” The Annals of Statistics, vol. 10, no. 4, Dec. 1982, doi: 10.1214/aos/1176345986.
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, Mar. 2010
T. H. Ali, “Modification of the adaptive Nadaraya-Watson kernel method for nonparametric regression (simulation study),” Communications in Statistics - Simulation and Computation, pp. 1–13, Aug. 2019, doi: 10.1080/03610918.2019.1652319.
Wolfgang Härdle, Applied nonparametric regression. Cambridge England; New York: Cambridge University Press, 1997.
W. Hardle, “Applied Nonparametric Regression.,” Biometrics, vol. 50, no. 2, p. 592, Jun. 1994, doi: 10.2307/2533418.
Copyright (c) 2021 Hazhar T. A. Blbas, Wasfi T. Kahwachi
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-ND 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).