A Comparison Between New Modification of Adaptive Nadaraya-Watson Kernel and Classical Adaptive Nadaraya-Watson Kernel Methods in Nonparametric Regression

A Simulation Study

  • Hazhar T. A. Blbas Department of Statistics, College of Administration and Economics, Salahaddin University-Erbil, ‎Kurdistan Region, Iraq ‎
  • Wasfi T. Kahwachi Research Center, Tishk International University-Erbil (TIU), Kurdistan Region, Iraq ‎ https://orcid.org/0000-0002-1610-2998
Keywords: Non-parametric Regression, Kernel Regression, New ANW Estimators, Leukemia Cancer, AML


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.


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‎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.‎

How to Cite
Blbas H, Kahwachi W. A Comparison Between New Modification of Adaptive Nadaraya-Watson Kernel and Classical Adaptive Nadaraya-Watson Kernel Methods in Nonparametric Regression. cuesj [Internet]. 30Oct.2021 [cited 16Apr.2024];5(2):32-7. Available from: https://journals.cihanuniversity.edu.iq/index.php/cuesj/article/view/483
Research Article