Robust algorithms for multiphase regression models |
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| Institution: | 1. Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, Taiwan;2. Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan;1. Department of Animal and Food Sciences, Oklahoma State University, Stillwater 74078;2. Livestock and Forestry Research Station, Division of Agriculture, University of Arkansas, Batesville 72501;3. Department of Animal Science, Division of Agriculture, University of Arkansas, Fayetteville 72701;1. School of Civil and Transportation Engineering, Hebei University of Technology, 5340 Xiping Road, Beichen District, Tianjin 300401, PR China;2. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, PR China;1. P.N. Lebedev Physical Institute of the RAS, Leninsky prosp. 53, Moscow 119991, Russia;2. Far Eastern Federal University, Sukhanova str. 8, Vladivostok 690090, Russia;3. Department of Energy, CIEMAT, Avda. Complutense 40, Madrid 28040, Spain;4. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia;2. Livestock and Forestry Research Station, Batesville, AR 72501;2. Livestock and Forestry Research Station, Division of Agriculture, University of Arkansas, Batesville 72501;3. Cooperative Extension Service, Bourbon County, University of Kentucky, Paris 40361;4. Department of Agronomy, The Pennsylvania State University, University Park 16802 |
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| Abstract: | This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach. |
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