Quantile Regression via the EM Algorithm |
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Authors: | Ying-hui Zhou Yong Li |
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Affiliation: | 1. School of Economics, Shanghai University, Shanghai 200444, China;2. Hanqing Advanced Institute of Economics and Finance, Renmin University, Beijing 100872, China |
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Abstract: | The three-parameter asymmetric Laplace distribution (ALD) has received increasing attention in the field of quantile regression due to an important feature between its location and asymmetric parameters. On the basis of the representation of the ALD as a normal-variance–mean mixture with an exponential mixing distribution, this article develops EM and generalized EM algorithms, respectively, for computing regression quantiles of linear and nonlinear regression models. It is interesting to show that the proposed EM algorithm and the MM (Majorization–Minimization) algorithm for quantile regressions are really the same in terms of computation, since the updating formula of them are the same. This provides a good example that connects the EM and MM algorithms. Simulation studies show that the EM algorithm can successfully recover the true parameters in quantile regressions. |
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Keywords: | Asymmetric Laplace distribution Generalized EM algorithm Generalized inverse Gaussian distribution MM algorithm Normal-variance–mean mixture. |
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