Smoothing parameter selection in Nadaraya-Watson kernel nonparametric regression using nature-inspired algorithm optimization.

Section: Research Paper
Issue
Vol. 17 No. 2 (2020): Volume 17 Issue 2
Published
Jun 25, 2025
Pages
43-50

Abstract

In the context of Nadaraya-Watson kernel nonparametric regression, the curve estimation is fully depending on the smoothing parameter. At this point, the nature-inspired algorithms can be used as an alternative tool to find the optimal selection. In this paper, a firefly optimization algorithm method is proposed to choose the smoothing parameter in Nadaraya-Watson kernel nonparametric regression. The proposed method will efficiently help to find the best smoothing parameter with a high prediction. The proposed method is compared with four famous methods. The experimental results comprehensively demonstrate the superiority of the proposed method in terms of prediction capability.

References

  1. Abramson, I. S. (1982). On bandwidth variation in kernel estimates-a square root law. The Annals of Statistics, 1217-1223.
  2. Ali, T. H. (2019). Modification of the adaptive Nadaraya-Watson kernel method for nonparametric regression (simulation study). Communications in Statistics - Simulation and Computation, 1-13. doi:10.1080/03610918.2019.1652319
  3. Chen, S. (2015). Optimal Bandwidth Selection for Kernel Density Functionals Estimation. Journal of Probability and Statistics, 2015, 1-21. doi:10.1155/2015/242683
  4. Chu, C. (1995). Bandwidth selection in nonparametric regression with general errors. Journal of statistical planning and inference, 44(3), 265-275.
  5. Chu, C.-K., & Marron, J. S. (1991). Comparison of two bandwidth selectors with dependent errors. The Annals of Statistics, 19(4), 1906-1918.
  6. Dobrovidov, A. V., & Rudsko, I. M. (2010). Bandwidth selection in nonparametric estimator of density derivative by smoothed cross-validation method. Automation and Remote Control, 71(2), 209-224. doi:10.1134/s0005117910020050
  7. Feng, Y., & Heiler, S. (2009). A simple bootstrap bandwidth selector for local polynomial fitting. Journal of Statistical Computation and Simulation, 79(12), 1425-1439. doi:10.1080/00949650802352019
  8. Fister, I., Fister, I., Yang, X.-S., & Brest, J. (2013). A comprehensive review of firefly algorithms. Swarm and Evolutionary Computation, 13, 34-46. doi:10.1016/j.swevo.2013.06.001
  9. Francisco-Fernndez, M., & Vilar-Fernndez, J. M. (2005). Bandwidth selection for the local polynomial estimator under dependence: a simulation study. Computational Statistics, 20(4), 539-558.
  10. Friedman, J. H., & Stuetzle, W. (1981). Projection pursuit regression. Journal of the American Statistical Association, 76(376), 817-823.
  11. Gao, J., & Gijbels, I. (2012). Bandwidth Selection in Nonparametric Kernel Testing. Journal of the American Statistical Association, 103(484), 1584-1594. doi:10.1198/016214508000000968
  12. Hazelton, M. L., & Cox, M. P. (2016). Bandwidth selection for kernel log-density estimation. Computational Statistics & Data Analysis, 103, 56-67. doi:10.1016/j.csda.2016.05.003
  13. Karthikeyan, S., Asokan, P., & Nickolas, S. (2014). A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints. The International Journal of Advanced Manufacturing Technology, 72(9-12), 1567-1579. doi:10.1007/s00170-014-5753-3
  14. Kauermann, G., & Opsomer, J. D. (2004). Generalized Cross-Validation for Bandwidth Selection of Backfitting Estimates in Generalized Additive Models. Journal of Computational and Graphical Statistics, 13(1), 66-89. doi:10.1198/1061860043056
  15. Kolek, J., & Horov, I. (2017). Bandwidth matrix selectors for kernel regression. Computational Statistics, 32(3), 1027-1046. doi:10.1007/s00180-017-0709-3
  16. Kyung Lee, Y., Park, B. U., & Su Park, M. (2007). A simple and effective bandwidth selector for local polynomial quasi-likelihood regression. Journal of Nonparametric Statistics, 19(6-8), 255-267. doi:10.1080/10485250701761086
  17. Lee, T. C., & Solo, V. (1999). Bandwidth selection for local linear regression: a simulation study. Computational Statistics, 14(4), 515-532.
  18. Leungi, D. H. Y., Marriott, F. H. C., & Wu, E. K. H. (1993). Bandwidth selection in robust smoothing. Journal of Nonparametric Statistics, 2(4), 333-339. doi:10.1080/10485259308832562
  19. Li, J., & Palta, M. (2009). Bandwidth selection through cross-validation for semi-parametric varying-coefficient partially linear models. Journal of Statistical Computation and Simulation, 79(11), 1277-1286. doi:10.1080/00949650802260071
  20. Nychka, D. (1991). Choosing a range for the amount of smoothing in nonparametric regression. Journal of the American Statistical Association, 86(415), 653-664.
  21. Opsomer, J. D., & Miller, C. P. (2007). Selecting the amount of smoothing in nonparametric regression estimation for complex surveys. Journal of Nonparametric Statistics, 17(5), 593-611. doi:10.1080/10485250500054642
  22. REFERENCES
  23. Rice, J. (1984). Bandwidth choice for nonparametric regression. The Annals of Statistics, 12(4), 1215-1230.
  24. Schucany, W. R. (1995). Adaptive Bandwidth Choice for Kernel Regression. Journal of the American Statistical Association, 90(430), 535-540. doi:10.1080/01621459.1995.10476545
  25. Scott, D. W., & Terrell, G. R. (1987). Biased and unbiased cross-validation in density estimation. Journal of the American Statistical Association, 82(400), 1131-1146.
  26. Silverman, B. W. (1986). Density estimation for statistics and data analysis (Vol. 26): CRC press.
  27. Slaoui, Y. (2016). Optimal bandwidth selection for semi-recursive kernel regression estimators. Statistics and Its Interface, 9(3), 375-388. doi:10.4310/SII.2016.v9.n3.a11
  28. Steland, A. (2012). Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction. Communications in Statistics - Simulation and Computation, 41(7), 1195-1219. doi:10.1080/03610918.2012.625853
  29. Utami, T. W., Haris, M. A., Prahutama, A., & Purnomo, E. A. (2020). Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods. Journal of Physics: Conference Series, 1446, 012049. doi:10.1088/1742-6596/1446/1/012049
  30. Yang, X.-S. (2013). Multiobjective firefly algorithm for continuous optimization. Engineering with Computers, 29(2), 175-184.
  31. Yelghi, A., & Kse, C. (2018). A modified firefly algorithm for global minimum optimization. Applied Soft Computing, 62, 29-44. doi:10.1016/j.asoc.2017.10.032
  32. Yoon Kim, T., & Park, C. (2002). Regression Smoothing Parameter Selection Using Cross Residuals Sum. Communications in Statistics - Theory and Methods, 31(12), 2275-2287. doi:10.1081/sta-120017225
  33. Zhang, Z. G., Chan, S. C., Ho, K. L., & Ho, K. C. (2008). On Bandwidth Selection in Local Polynomial Regression Analysis and Its Application to Multi-resolution Analysis of Non-uniform Data. Journal of Signal Processing Systems, 52(3), 263-280. doi:10.1007/s11265-007-0156-4
  34. Zhou, H., & Huang, X. (2018). Bandwidth selection for nonparametric modal regression. Communications in Statistics - Simulation and Computation, 48(4), 968-984. doi:10.1080/03610918.2017.1402044
  35. ychaluk, K. (2014). Bootstrap bandwidth selection method for local linear estimator in exponential family models. Journal of Nonparametric Statistics, 26(2), 305-319. doi:10.1080/10485252.2014.885023

Authors

Zakariya Yahya Algamal

Dept. of Statistics and Informatics/ college of computer sciences and mathematics/ University of Mosul, Mosul, iraq

ORCID
Zinah Basheer

Department of Statistics and Informatics, Computer science and Mathematics, University of Mosul, Mosul, Iraq

Identifiers

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How to Cite

Yahya Algamal, Z., زکریا, Basheer, Z., & زینة. (2025). Smoothing parameter selection in Nadaraya-Watson kernel nonparametric regression using nature-inspired algorithm optimization. IRAQI JOURNAL OF STATISTICAL SCIENCES, 17(2), 43–50. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20762