International Journal of Nonlinear Analysis and Applications

Robust estimates for a three-parameter exponential regression model

Document Type : Research Paper

Authors

Statistics Department, College of Administration and Economics, University of Baghdad, Iraq

Abstract

Exponential regression is one of the most common and widely used models in several fields to estimate the parameters of the exponential regression model using ordinary nonlinear least square but this method is not effective in the presence of outlier values so robust methods were used to treat outlier values in this research exponential regression model are used to estimate the parameters using robust method (Median-of-Means, Forward search, M-Estimation), and the simulation method was used to compare the estimation methods with different sample sizes and assuming four percentages of the outliers of the data (10%, 20%, 30%, 40%). And through the mean square error (MSE) was made to reach the best estimation method for the parameters, where the results obtained using the simulation method showed that the forward search is the best because it gives the lowest mean of error squares.

Keywords

[1] J.A. Achcar and S.R.C. Lopes, Linear and non-linear regression models assuming a stable distribution, Colomb. J. Statist. 39 (2016), no. 1, 109–128.
[2] A.C. Atkinson, A. Corbellini and M. Riani, Robust Bayesian regression with the forward search: theory and data analysis, Test 26 (2017), no. 4, 869–886.
[3] A.C. Atkinson, M. Riani and A. Cerioli, The forward search: Theory and data analysis, J. Korean Statist. Soc. 39 (2010), 117–134.
[4] R. Koenker and B.J. Park, An interior point algorithm for nonlinear quantile regression, J. Econometr. 71 (1996), 265–283.
[5] M. Lerasle, Selected topics on robust statistical learning theory lecture notes, Paris-Saclay University, 2019.
[6] P. Liu, M. Zhang, R. Zhang and Q. Zhou, Robust estimation and tests for parameters of some nonlinear regression models, J. Math. 9 (2021).
[7] R. Meyer and P.M. Roth, Modified damped least squares: an algorithm for non-linear estimation, J. Inst. Maths. Appl. 9 (1972), 218–233.
[8] M. Rian and A.C. Atkinso, Robust diagnostic data analysis: transformations in regression’ technometrics, Amer. Statist. Assoc. Amer. Soc. Qual. 42 (2000), no. 4, 384–394.
[9] G.A.F. Seber and C.J. Wild, Nonlinear regression, John Wiley & Sons Inc., 2003.
[10] Y. Zhang and P. Liu, Median-of-means approach for repeated measures data, Commun. Statistics-Theory Meth. 50 (2021), no. 17, 3903–3912.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 2799-2808
  • Receive Date: 13 November 2022
  • Revise Date: 23 December 2022
  • Accept Date: 02 January 2023