SUGGESTING MULTIPHASE REGRESSION MODEL ESTIMATION WITH SOME THRESHOLD POINT

admin February 27, 2020

Authors:

Omar Abdulmohsin Ali,

DOI NO:

https://doi.org/10.26782/jmcms.2020.02.00019

Keywords:

Data-driven strategy,kernel,multiphase regression,robustness,threshold point,winsorization,

Abstract

The estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of this paper is to suggest a new hybrid estimator obtained by an ad-hoc algorithm which relies on data driven strategy that overcomes outliers. While the minor goal is to introduce a new employment of an unweighted estimation method named "winsorization"  which is a good method to get robustness in regression estimation via special technique to reduce the effect of the outliers. Another specific contribution in this paper is to suggest employing "Kernel" function as a new weight (in the scope of the researcher's knowledge).Moreover, two weighted estimations are based on robust weight functions named "Cauchy" and "Talworth". Simulations have been constructed with contamination levels (0%, 5%, and 10%) which associated with sample sizes (n=40,100). Real data application showed the superior performance of the suggested method compared with other methods using RMSE and R² criteria.

Refference:

I. Acitas, S. and Senoglu, B., (2020). “Robust change point estimation in two-phase linear regression models: An application to metabolic pathway data”. Journal of Computational and Applied Mathematics, Vol. 363, pp 337–349.

II. Chen, C.W.S., Chan, J. S.K., Gerlach, R., and Hsieh, W. Y.L., (2011). “A comparison of estimators for regression models with change points”. Stat Comput, Vol. 21, pp 395–414.

III. Dehnel, G., (2016). “M-Estimators in Business Statistics”.Statistics in Transition new series, Vol. 17, No. 4, pp 1–14.

IV. Fearnhead, P. and Rigaill, G., (2017). “Changepoint Detection in the Presence of Outliers”.Journal of the American Statistical Association, Vol. 114, No. 525, pp 169-183.

V. Ganocy, S. J. and Sun, J., (2015). “Heteroscedastic Change Point Analysis and Application to Footprint Data”.Journal of Data Science, Vol. 13, pp 157-186.

VI. Hernandez, E.L., (2010). ” Parameter Estimation in Linear-LinearSegmentedRegression. M.Sc. thesis, Department of Statistics, Brigham Young University,

VII. Julious, S.A., (2001). “Inference and Estimation in a Change point Regression Problem”. The Statistician, Vol. 50, Part 1, pp 51-61.

VIII. Klotsche, J. and Gloster, A. T., (2012). “Estimating a Meaningful Point of Change:A Comparison of Exploratory Techniques Based on Nonparametric Regression”. Journal of Educational and Behavioral Statistics Vol. 37, pp 579-600.

IX. Liu, Z., (2011). “Empirical Likelihood Method for Segmented Linear Regression”.Ph.D. Dissertation, Faculty of the Charles E. Schmidt, College of Science, Florida Atlantic University, USA.

X. Muggeo, V. M. R., (2003). “Estimating regression models with unknown break-points”, Statist.Med., Vol. 22, pp 3055–3071.

XI. Muggeo, V. M. R., (2017).”Interval estimation for the breakpoint in segmented regression: a smoothed score-based approach”. Aust. N. Z. J. Stat. Vol. 59, No.3, pp 311–322.

XII. Pusparum, M., (2017). “Winsor Approach in Regression Analysis with Outlier”.Applied Mathematical Sciences, Vol. 11, No. 41, pp 2031-2046.

XIII. Ryan, S.E. and Porth, L. S., (2007). “A Tutorial on the Piecewise Regression Approach Applied to Bedload Transport Data”. General Technical Report RMRS-GTR-189. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 41 p.

XIV. Whitehead, N., Hill, H.A., Brogan, D.J. and Blackmore-Prince, C., (2002). Exploration of threshold analysis in the relation between stressful life events and preterm delivery”. American Journal of Epidemiology Vol. 155, pp 117–124.

XV. Yale, C. and Forsythe, A.B., (1976). “Winsorized Regression”, Technometrics, Vol.18 No.3, pp 291-300.

XVI. Zhang, F., Li, Q.,(2017).”Robust bent line regression”. J. Statist. Plann. Inference, Vol.185,pp41-55.

View Download