New Huber weighted function based on wavelet process in robust estimation: A Simulation Study
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Abstract
One of the primary problems affecting the accuracy of linear regression parameter estimates is contamination, including noise and outliers. To reduce the impact of data contamination, a novel Huber-weighted function based on wavelet processing is evaluated in this study and compared with the classical Huber-weighted function. The efficiency of the suggested approach is demonstrated through simulation, which also compares it with the traditional Huber method using the root-mean-square errors of the calculated parameters. A simulation program was implemented using MATLAB. The study's findings demonstrated that the suggested approach effectively handled contamination (noise and outliers) and improved the precision of the multiple linear regression's parameter estimates when outliers were present.
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Alma, Ö. G. (2011). Comparison of robust regression methods in linear regression. Int. J. Contemp. Math. Sciences, 6(9), 409-421.
Ali, (2019) Choice the best estimations of parameters robust regression model with practical application. Journal of statistical Theory, 59, 114-129.
Ali, T. H., & Saleh, D. M. (2022). Proposed hybrid method for wavelet shrinkage with robust multiple linear regression model: With simulation study. Qalaai Zanist Journal, 7(1), 920-937.
Al-Azzawi, E. A., & Al-Always, L. A. (2022). Robust Estimation OF the Partial Regression Model Using Wavelet Thresholding. Journal of Economics and Administrative Sciences, 28(133), 97-113.
Amin, L. D. H. A. (2022). Regression Techniques for Analysis of Variance with Application to the Reduction on Serum Cholesterol Level. Tikrit Journal of Administrative and Economic Sciences, 18(57 part 2).
Čížek, P. (2011). Semi-parametrically weighted robust estimation of regression models. Computational Statistics & Data Analysis, 55(1), 774-788.
Choi, S.W., 2009. The effect of outliers on regression analysis: regime type and foreign direct investment. Quarterly Journal of Political Science, 4(2), pp.153-165
Daubechies, I. (1992). Ten lectures on wavelets. Society for Industrial and Applied Mathematics, pp.17-52, pp.53-106.
Fox, J. (2002). An R and S-Plus companion to applied regression, 91(2), p.6.
Gençay, R., Selçuk, F., & Whitcher, B. J. (2001). An introduction to wavelets and other filtering methods in finance and economics. Elsevier.
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity. Monographs on statistics and applied probability, 143(143), 8.
Ismael, A. A., & Albairmani, Z. A. (2021). The effect of some independent variables on granting the basic application certificate using multivariate statistical analysis. Tikrit Journal of Administrative and Economic Sciences, 17(54 part 3).
Jianhui, X., & Li, T. (2019, December). Image denoising method based on improved wavelet threshold transform. In 2019 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1064-1067). IEEE.
[14] Kumar, A., & Kusagur, A. (2018). Soft thresholding-based image denoising algorithm. International Journal of Scientific and Engineering Research, 9(7), 1041-1043.
kanamori, T. & fujisawa, H. (2015) "Robust estimation under heavy contamination using unnormalised models. Biormetrika (2015), 102, 3, pp. 559–572.
Omer, A. W., Sedeeq, B. S., & Ali, T. H. (2024). A proposed hybrid method for multivariate linear regression model and multivariate wavelets (simulation study). Mitanni Journal of Humanitarian Sciences, 5(1), 112-124.
Peng, L., Liu, X., & Lian, H. (2024). Functional Adaptive Huber Linear Regression. arXiv preprint arXiv:2409. 11053..
Prasetya, R. P. (2022). Unpacking Outlier with Weighted Least Squares (Implemented on Pepper Plantations Data). Parameter: Journal of Statistics, 2(3), 24-31.
Qadir, J. R. (2022). Using Wavelet Shrinkage in the Cox Proportional Hazards Regression model (simulation study). Iraqi Journal of Statistical Sciences, 19(1), 17-29.
Susanti, Y., Pratiwi, H., Sulistijowati, S., & Liana, T. (2014). M estimation, S estimation, and MM estimation in robust regression. international Journal of pure and applied mathematics, 91(3), 349-360.
Saputri, S. (2023). Regression Analysis of Robust Estimates with Tukey Bisquare Weighting on Poverty Level on Sulawesi Island. Parameter: Journal of Statistics, 3(2), 84-92.
Feng, Y., & Wu, Q. (2022). A statistical learning assessment of Huber regression. Journal of Approximation Theory, 273, 105660.
Sulaiman, N.G. and Rahim, A.G., (2022). Using A Proposed Method for Wavelet Shrinkage to Estimate the Tuning Parameter of Penalised Linear Regression. PalArch's Journal of Archaeology of Egypt/Egyptology, 19(3), pp.424-439.
Susanti, Y., Pratiwi, H., Sulistijowati, S., & Liana, T. (2014). My estimation, S estimation, and MM estimation in robust regression. international Journal of pure and applied mathematics, 91(3), 349-360.
Salh, A. P. D. S. M., Abdalla, H. T., & Omer, Z. M. (2021). Using a Multinomial Logistic Regression model to study factors that affect chest pain. Tikrit Journal of Administrative and Economic Sciences, 17(53 part 2).
Saputri, S., 2023. Regression Analysis of Robust Estimation-S with Tukey Bisquare Weighting On Poverty Level On Sulawesi Island. Parameter: Journal of Statistics, 3(2), Pp.84-92.
Yulita, T., Notodiputro, K. A., & Sadik, K. (2018). M-estimation uses bisquare, Hampel, Huber, and Welsch weight functions in robust regression. Int. J. Sci. Res. Sci. Eng. Technol, 4(9), 425-430.