A gradient search maximization algorithm for the asymmetric Laplace likelihood

作者：Bottai Matteo^*; Orsini Nicola; Geraci Marco

来源：Journal of Statistical Computation and Simulation, 2015, 85(10): 1919-1925.

DOI：10.1080/00949655.2014.908879

• mixed-effects quantile regression
• quantile regression
• direct search optimization algorithms
• Laplace regression
• asymmetric Laplace distribution

The asymmetric Laplace likelihood naturally arises in the estimation of conditional quantiles of a response variable given covariates. The estimation of its parameters entails unconstrained maximization of a concave and non-differentiable function over the real space. In this note, we describe a maximization algorithm based on the gradient of the log-likelihood that generates a finite sequence of parameter values along which the likelihood increases. The algorithm can be applied to the estimation of mixed-effects quantile regression, Laplace regression with censored data, and other models based on Laplace likelihood. In a simulation study and in a number of real-data applications, the proposed algorithm has shown notable computational speed.

• 出版日期2015-7-3