Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression

@article{Bera2015AsymmetricLR,
  title={Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression},
  author={Anil K. Bera and Antonio F. Galvao and Gabriel Montes-Rojas and Sung Yong Park},
  journal={Journal of Econometric Methods},
  year={2015},
  volume={5},
  pages={101 - 79}
}
This paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile… CONTINUE READING

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