Parameters Estimation of the Fractional Trigonometric Polynomial Regression Model Using Maximum Likelihood and Bootstrap Methods
DOI:
https://doi.org/10.31272/jae.i151.1511Keywords:
Fractional Trigonometric Regression, Maximum Likelihood, Bootstrap, Statistical Estimation, DiabetesAbstract
This study aims to examine the Fractional Trigonometric Polynomial Regression Model as a nonlinear statistical model for representing complex relationships between dependent and independent variables. Two estimation methods were used: the Maximum Likelihood (ML) and Bootstrap methods. Simulation experiments with different sample sizes were conducted to compare their performance in parameter estimation. The results showed that the ML method performed better when the variance was low, whereas the Bootstrap method was more accurate when the variance was high. The model was also applied to real data of diabetic patients, and the findings confirmed that the data follow a normal distribution and that the proposed model provides a precise representation of the relationships among variables
Downloads
References
[1] Royston, P., & Altman, D. G. (1994). Regression using fractional polynomials of continuous covariates: Parsimonious parametric modelling. Journal of the Royal Statistical Society: Series C (Applied Statistics), 43(3), 429–467. DOI: https://doi.org/10.2307/2986270 DOI: https://doi.org/10.2307/2986270
[2] Ishola, T. A., Olatayo, O. T., & Adesanya, K. K. (2019). Parameter estimation of fractional trigonometric polynomial regression model. International Journal of Computers, 5, 19-25. Link: https://www.iaras.org/iaras/journals/ijc .
[3] Duong, H., & Volding, D. (2014). Modelling continuous risk variables: Introduction to fractional polynomial regression. Vietnam Journal of Science (VJS), 1(2). Link: https://vietnamresearch.com/vjs/
[4] Ullah, E., & Shah, T. (2014). Trigonometric polynomial rings and their factorization properties. Matematički Vesnik, 66(3), 301–314. DOI: https://doi.org/10.2298/MEV1403301U
[5] Ahmed, A. D., & Kazem, G. A. S. (2017). Estimation of parameters of the second-degree multivariate polynomial regression model with a practical application. Al-Qadisiyah Journal of Administrative and Economic Sciences, 19(3), 376–398. Link (IASJ): https://www.iasj.net/iasj/article/133719
[6] Baneshi, M. R., Nakhaee, F., & Law, M. (2013). On the use of fractional polynomial models to assess preventive aspect of variables: An example in prevention of mortality following HIV infection. International Journal of Preventive Medicine, 4(4), 414–419. DOI: https://doi.org/10.4103/2008-7802.111820
[7] Royston, P., Ambler, G., & Sauerbrei, W. (1999). The use of fractional polynomials to model continuous risk variables in epidemiology. International Journal of Epidemiology, 28(5), 964–974. DOI: https://doi.org/10.1093/ije/28.5.964 DOI: https://doi.org/10.1093/ije/28.5.964
[8] Morris, T. P., White, I. R., Carpenter, J. R., Stanworth, S. J., & Royston, P. (2015). Combining fractional polynomial model building with multiple imputation. Statistics in Medicine, 34(21), 3298–3317. DOI: https://doi.org/10.1002/sim.6549 DOI: https://doi.org/10.1002/sim.6553
[9] Eubank, R.L, & Speckman, P. (1987). Data Smoothing by polynomial-trigonometric regression. Technical Report No. SWI/DS/TR/212, Southern Methodist University.
[10] Ali, O. A., & Kazem, K. J. (2019). Using the maximum likelihood method with a proposed weight to estimate the effect of some pollutants in the Tigris River – Kut city. Journal of Administration and Economics, 42(120). Link (IASJ): https://www.iasj.net/iasj/article/171549
[11] Barrios, E. B. (2011). Bootstrap methods. The Philippine Statistician, 60(1), 129–132. Link: https://psa.gov.ph/sites/default/files/ThePhilippineStatistician_2011_60_1_11.pdf DOI: https://doi.org/10.59139/ws.2011.11.6
[12] Ahmed, S. A. (2018). Estimation of simple linear regression model parameters using the bootstrap method under heteroscedasticity. Scientific Journal of Faculty of Commerce, Alexandria University, 55(2), 184–511. Link: https://acj.journals.ekb.eg/
[13] Ahmed, A. D., & Rahman, M. A. R. (2019). Comparison of modified maximum likelihood methods for estimating autoregressive model parameters. Journal of Administration and Economics, University of Baghdad, 42(120), 305–318. Link (IASJ): https://www.iasj.net/iasj/article/171561
[14] Das, K. R., & Imon, A. H. M. R. (2016). A brief review of tests for normality. American Journal of Theoretical and Applied Statistics, 5(1), 5–12. DOI: https://doi.org/10.11648/j.ajtas.20160501.12 DOI: https://doi.org/10.11648/j.ajtas.20160501.12
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Zahraa Mohammed Mahmoud Al-Najjar, & Ahmed Theyab Ahmed
This work is licensed under a Creative Commons Attribution 4.0 International License.
The journal of Administration & Economics is an open- access journal that all contents are free of charge. Articles of this journal are licensed under the terms of the Creative Commons Attribution International Public License CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/legalcode) that licensees are unrestrictly allowedto search, download, share, distribute, print, or link to the full text of the articles, crawl them for indexing and reproduce any medium of the articles provided that they give the author(s) proper credits (citation). The journal allows the author(s) to retain the copyright of their published article.
Creative Commons-Attribution (BY) 
