Volume 26 , Issue 2 , PP: 215-228, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Kesavulu Poola 1 , V. Pavankumari 2 , J. Anil Kumar 3 , Akkyam Vani 4 , Asif Alisha S. 5 , A. Srinivasulu 6
Doi: https://doi.org/10.54216/IJNS.260216
Regression modeling is a significant statistical tool aimed at quantifying and understanding the nature of relations between the predictor and response variables. The routine parameter estimation procedures, like OLS and ML, are based heavily on the assumption of normality in data, which will not be the case for most real-world data scenarios. The paper presents a Neutrosophic approach for the estimation of parameters in multiple linear regression models, making use of the Neutrosophic principles to treat uncertainties, indeterminacies, and inconsistencies in actual data, a proposed method is called the Simple Averaging Method, or SAM. This is a robust alternative to traditional methods and provides reliable results even if the assumptions of normality are not held. SAM performance is tested using real-time crime data in the USA and demonstrates its capabilities to deal with complex datasets. The comparative analysis between the OLS model and the same model is done via RMSE and MAD metrics. The results show that SAM significantly outperforms OLS with an RMSE of 34.37598 in contrast to 58.05248 for OLS. Graphical analysis further confirms SAM's performance over and above OLS. Critical issues of regression modeling with incorporation of neutrosophic logic cover their critical challenges, especially when standard assumptions are violated.
Simple Averaging Method , Ordinary Least Squares method (OLS) , Maximum likelihood estimation (MLE) , RMSE , MAE
[1] A. M. Variyath and A. Brobbey, "Variable selection in multivariate multiple regression," PLoS One, vol. 15, no. 7, Jul. 2020, doi: 10.1371/journal.pone.0236067.
[2] P. Balestra, "On the efficiency of ordinary least-squares in regression models," J. Am. Stat. Assoc., vol. 65, no. 331, pp. 1330–1337, 1970, doi: 10.1080/01621459.1970.10481168.
[3] B. Gafarov, "Generalized Automatic Least Squares: Efficiency Gains from Misspecified Heteroscedasticity Models," arXiv preprint arXiv: 2304.07331, Apr. 2023. [Online]. Available: https://arxiv.org/abs/2304.07331
[4] D. Chicco, M. J. Warrens, and G. Jurman, "The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation," PeerJ Comput. Sci., vol. 7, pp. 1–24, 2021, doi: 10.7717/peerj-cs.623.
[5] Ö. Türkşen, "A novel perspective for parameter estimation of seemingly unrelated nonlinear regression," J. Appl. Stat., vol. 48, no. 13–15, pp. 2326–2347, 2021, doi: 10.1080/02664763.2021.1877638.
[6] M. R. Abonazel and I. M. Taha, "Beta ridge regression estimators: simulation and application," Commun. Stat. Simul. Comput., vol. 52, no. 9, pp. 4280–4292, 2023, doi: 10.1080/03610918.2021.1960373.
[7] S. D. Permai and H. Tanty, "Linear regression model using Bayesian approach for energy performance of residential building," in Procedia Comput. Sci., Elsevier B.V., 2018, pp. 671–677, doi: 10.1016/j.procs.2018.08.219.
[8] Y. M. Al-Hassan, "Performance of a new ridge regression estimator," J. Assoc. Arab Univ. Basic Appl. Sci., vol. 9, no. 1, pp. 23–26, 2010, doi: 10.1016/j.jaubas.2010.12.006.
[9] M. S. Khan, A. Ali, M. Suhail, E. S. Alotaibi, and N. E. Alsubaie, "On the estimation of ridge penalty in linear regression: simulation and application," Kuwait J. Sci., vol. 51, no. 4, Oct. 2024, doi: 10.1016/j.kjs.2024.100273.
[10] Y. J. Lei, B. Y. Wang, and Y. T. Yang, "Optimizing the loss function for bounding box regression through scale smoothing," Ain Shams Eng. J., Nov. 2024, doi: 10.1016/j.asej.2024.103046.
[11] A. Yalçınkaya, İ. G. Balay, and B. Şenoğlu, "A new approach using the genetic algorithm for parameter estimation in multiple linear regression with long-tailed symmetric distributed error terms: an application to the COVID-19 data," Chemom. Intell. Lab. Syst., vol. 216, Sep. 2021, doi: 10.1016/j.chemolab.2021.104372.
[12] S. Acitas, P. Kasap, B. Senoglu, and O. Arslan, "One-step M-estimators: Jones and Faddy’s skewed t-distribution," J. Appl. Stat., vol. 40, no. 7, pp. 1545–1560, 2013, doi: 10.1080/02664763.2013.788620.
[13] K. Poola, J. Anil Kumar, V. Pavankumari, P. Hemalatha, and N. M. Bhupathi, "Testing of multivariate nonlinear regression hypothesis using nonlinear least square (NLS) estimation," Int. J. Stat. Appl. Math., vol. 5, no. 6, pp. 147–150, 2020.
[14] A. J. Telmoudi, M. Soltani, L. Chaouech, and A. Chaari, "Parameter estimation of nonlinear systems using a robust possibilistic c-regression model algorithm," Proc. Inst. Mech. Eng. I J. Syst. Control Eng., vol. 234, no. 1, pp. 134–143, Jan. 2020, doi: 10.1177/0959651818756246.
[15] A. Prabowo, A. Sugandha, A. Tripena, M. Mamat, Sukono, and R. Budiono, "A new method to estimate parameters in the simple regression linear equation," Math. Stat., vol. 8, no. 2, pp. 75–81, 2020, doi: 10.13189/ms.2020.080201.
[16] A. D. Al-Nasser and A. Radaideh, "Estimation of simple linear regression model using L-ranked set sampling," 2008.
[17] H.-H. Huang and Q. He, "Nonlinear Regression Analysis," Feb. 2024, doi: 10.1016/B978-0-12-818630-5.10068-5.
[18] F. Prihatmono, M. Y. Darsyah, and A. Karim, "Residual bootstrap resampling method for multiple linear regression model parameter estimation," J. Litbang Edusaintech, vol. 1, no. 1, pp. 35–43, Dec. 2020, doi: 10.51402/jle.v1i1.8.
[19] P. H. Sekhar, H. Sekhar, K. Poola, and B. Naidu, "Combined multiple forecasting model using regression," Int. J. Stat. Appl. Math., vol. 5, no. 6, pp. 147–150, 2020.
[20] M. R. Abonazel, Z. Y. Algamal, F. A. Awwad, and I. M. Taha, "A new two-parameter estimator for beta regression model: Method, simulation, and application," Front. Appl. Math. Stat., vol. 7, Jan. 2022, doi: 10.3389/fams.2021.780322.
[21] P. Kesavulu, M. Bhupathi Naidu, and P. Balasiddamuni, "Impact Factor: 5.2 IJAR," Int. J. Appl. Res., vol. 2, no. 12, pp. 506–509, Nov. 2016.
[22] T. O. Hodson, "Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not," Jul. 2022, doi: 10.5194/gmd-15-5481-2022.
[23] J. Singthongchai, N. Thongmual, and N. Nitisuk, "An improved simple averaging approach for estimating parameters in simple linear regression model," Math. Stat., vol. 9, no. 6, pp. 939–946, Nov. 2021, doi: 10.13189/ms.2021.090610.
[24] S. Yasin, S. Kamal, and M. Suhail, "Performance of some new ridge parameters in two-parameter ridge regression model," Iran J. Sci. Technol. Trans. A Sci., vol. 45, no. 1, pp. 327–341, Feb. 2021, doi: 10.1007/s40995-020-01019-7.
[25] R. M. Dudley, "The speed of mean Glivenko-Cantelli convergence," Ann. Math. Stat., vol. 40, no. 1, pp. 40–50, 1969, doi: 10.1214/aoms/1177698212.
[26] M. J. Wainwright, "High-dimensional statistics: A non-asymptotic viewpoint," Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, 2019, doi: 10.1017/9781108627771.
[27] G. C. Calafiore and L. El Ghaoui, "Optimization Models," Encyclopedia of Systems and Control, pp. 1–8, Springer, 2021, doi: 10.1007/978-1-4471-5102-9_237-2.