A proposal to Employ the Laplace Estimator and the IRWL Algorithm as Robust Methods in Segmented Linear Regression and Compare them with the Maximum Likelihood Estimator using Simulation
DOI:
https://doi.org/10.62933/xja4cq74Keywords:
segmented linear regression, Join points, Iterative algorithm, Laplace estimator, , weighted least squaresAbstract
Segmented linear regression is one of the important statistical tools that is used to model and explain the behavior of some events in which changes gets suddenly or the behavior pattern of the event goes through transitional stages. The importance of this research lies in studying the proposal to employ the robust Laplace estimator within the method of estimating the parameters of the segmented linear regression model to give robustness to the estimation when there are outliers in the data. Then some updates were made to this method according to the iterative algorithm (IRWL) to get better robust estimates. On the practical side, the simulation experiment was conducted with several different sample sizes, and assuming several cases of pollution rates in the data (outliers) (15%, 10%, 5%, 0%), Then After implementing the simulation experiment and comparing the proposed methods with Muggeo's Maximum likelihood (ML) method using the (MSE) criterion, The experimental results showed the efficiency of the proposed methods when the data contains pollution ratios, and the iterative algorithm (IRWL) has proven its efficiency in obtaining the best estimate of the parameters compared to other methods. If there is no pollution in the data, the Muggeo's maximum likelihood (ML) method is the best for estimation.
References
[1] Acitas, S., Senoglu, B.(2020),”Robust change point estimation in two phase linear regression models:An application to metabolic pathway data”,Journal of Computational & Applied Mathematics,Vol.363,p. 337–349.
[2] Ahmed, A.D, Abdulwahhab, B.I, Abdulah, E.K.(2020),” A comparison among Different Methods for Estimating Regression Parameters with Autocorrelation Problem under Exponentially Distributed Error”, Baghdad Science Journal, Vol. 17, no. 3, p. 980-987.
[3] Ahmed. I.H. Shehab. D.H.(2017),”A Comparison between Methods of Laplace Estimators and the Robust Huber for Estimate parameters logistic regression model”, journal of Economics & Administrative Sciences, Vol. 23, no. 101, p. 524-547.
[4] Ali, O.A., Abbas, M.A. (2019),”New Robust Estimator Of Change Point In Segmented Regression Model For Bes-Load Of Rivers”, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6, p. 384-402.
[5] Box, G.E., Muller, M.E.(1958),”A note On The Generation Of Random Normal Deviates”, Ann. Math. Stat., 29, p. 610-611.
[6] Chen, C.W.S., Chan, J.S.K., So, M.K.P. and Lee, K.K.M.(2011), “Classification in segmented regression problems”, Computational Statistics and Data Analysis, 55, P. 2276–2287.
[7] Diniz, C.A.R., Milan, L.A. and Mazucheli, J.(2003),”Bayesian
inference of a linear segmented regression model”,Brazilian Journal of Probability & Statistics,17, p. 1–16.
[8] Gbur, E.E., Dahm, P.F.(1985),”Estimation of the linear-linear segmented regression model in the presence of measurement error”, Communications in Statistics-Theory and Methods,14(4),p. 809-826.
[9] Kim, H.J., Fay, M.P., Yu, B., Barrett, M.J. and Feuer, E.J.(2004), “Comparability of segmented line regression models”, Biometrics, 60,P. 1005–1014.
[10] Lu, KP., Chang, ST.(2020),”Robust algorithms for multiphase regression models”, Applied Mathematical Modelling,77, p.1643–1661.
[11] Muggeo, V. M.R.(2003),”Estimating regression models with unknown breakpoints”, Statistics in Medicine, 22, P. 3055–3071.
[12] Quandt, R.E.(1958),”The estimation of the parameters of a linear regression system obeying two separate regimes”, J. Amer. Statist. Assoc,53,P. 873–880.
[13] Ramsy, J.O.(1977),"A Comparative Study of Several Robust Estimates of Slope, Intercept, and Scale in Linear Regression", JASA, Vol. 72, no. 359, p. 608-615.
[14] Rousseeuw, P.J. and Leroy, A.(1987),"Robust regression and Outlier Detection", John Wiley and Sons.
[15] Shi, S., Li, Y. and Wan, C.(2018),”Robust continuous piecewise linear regression model with multiple change points”,The Journal Of Supercomputing.
[16] Yu, B., Barrett, M. J., Kim, H.-J. and Feuer, E.J.(2007),”Estimating join points in continuous time scale for multiple change-point models”, Computational Statistics and Data Analysis, 51, p. 2420–2427.
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