Investigation of Parametric, Non-Parametric and Semiparametric Methods in Regression Analysis

Year 2022, Volume 26, Issue 6, 1111 - 1116, 31.12.2022

Esra YAVUZ Mustafa ŞAHİN

https://doi.org/10.16984/saufenbilder.1147135

Abstract

Regression analysis is known as statistical methods applied to model and analyze the relationship between variables. Regression method can be examined as parametric, non-parametric and semiparametric regression methods. The parametric regression method assumes that the dependent variable is in a linear relationship with the independent variables and that the shape of the relationship is known. If these assumptions are not met, non-parametric regression methods are applied. However, these methods cause difficulties especially in the interpretation part due to the problem of multidimensionality when there is more than one independent variable. Thus, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while the other part may be in a nonlinear relationship. Thus, in order to model these relationships, semiparametric regression methods, which are the additive combination of parametric and non-parametric regression methods, are used. In this study, parametric regression method, definition of non-parametric regression method and assumption conditions are given. It has been shown that the semiparametric regression method can be applied in cases where these assumptions are not met. Thus, in the study, regression methods were examined in three different parts, and parametric, non-parametric and semiparametric regression methods were examined theoretically.

Keywords

Parametric, non-parametric, semiparametric, regression

References

• [1] G. Aneiros-Pérez, P. Vieu, “Nonparametric time series prediction: A semi-functional partial linear modeling”, J. Multivariate Anal, 99(5): 834-857, 2008.
• [2] M. Aytaç, “Applied non-parametric statistical tests”, Uludag University Press, Bursa, Turkey, 1991.
• [3] J. Begun, W. Hall, W. Huang, J. Wellner, “Information and asymptotic efficiency in parametric-nonparametric models”, Annals of Stat, 11: 432-452, 1983.
• [4] M. Çitil, F. Tuğrul, “Some New Equalities On the Intutionistic Fuzzy Modal Operators”, Sakarya University Journal of Science, 22(6), 2018.
• [5] J, Harezlak, D. Ruppert, M.P. Wand, “Semiparametric regression with R”, New York: Springer, 2018.
• [6] L. Keele, “Semiparametric Regression For The Social Sciences”, Chichester: John Wiley & Sons, 2008.
• [7] R. Li, H. Liang, “Variable selection in semiparametric regression modeling”, Annals of statistics, 36(1), 261, 2008.
• [8] D.Y. Lin, L.J. Wei, I. Yang, Z. Ying, “Semiparametric regression for the mean and rate functions of recurrent events”, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(4), 711-730, 2000.
• [9] J. Liu, R. Zhang, W. Zhao, “A robust and efficient estimation method for single index models”. J Multivariate Anal, 122: 226-238, 2013.
• [10] M. Mammadov, A.F. Yüzer, D. Aydın, “Splayn correction regression and correction parameter selection”, 4th Statistics Congress proceedings and poster abstracts book, Belek-Antalya, September 25-28, 2005, pp: 148-149, 2005.
• [11] X. Shi, “ Applications of nonparametric and semiparametric methods in economics and finance”. PhD Thesis, Economics in the Graduate School of Binghamton University, New York, 2009.
• [12] D. Ruppert, M.P. Wand, R.J. Carroll, “ Semiparametric regression” (No. 12). Cambridge university press, 2003.
• [13] X. Shi, “ Applications of nonparametric and semiparametric methods in economics and finance”. PhD Thesis, Economics in the Graduate School of Binghamton University, New York, 2009.
• [14] N. Tezcan, “Non-parametric regression analysis”. Atatürk Univ J Econ Admin Sci, 25: 341-352, 2011.
• [15] S. Toprak, “Semi-parametric regression models with measurement errors”. PhD Thesis, Dicle University, Institute of Science, Department of Mathematics, Diyarbakır, Turkey, pp: 98, 2015.
• [16] A. Yatchew, “Semiparametric regression for the applied econometrician”. Cambridge University Pres, Cambridge, UK, pp: 213, 2003.
• [17] E. Yavuz, M. Şahin, “ Semiparametric Regression Models and Applicability in Agriculture”. Black Sea Journal of Agriculture, 9-10, 2022.
• [18] Z. Zhongyi, W. Baocheng, “Dianostic and influence analysis for semiparametric nonlinear regression models”. Acta Math Appl Sinica, 24(4): 568-581, 2001.
• [19] M. Turanı, S. Bağdatlı, “Semiparametric Regression”. Suggestion Journal, 9(35), 207-213, 2011.