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.
A gradient search maximization algorithm for the asymmetric Laplace likelihood / Bottai, M; Orsini, N; Geraci, M. - In: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION. - ISSN 0094-9655. - 85:10(2014), pp. 1919-1925. [10.1080/00949655.2014.908879]
A gradient search maximization algorithm for the asymmetric Laplace likelihood
GERACI M
2014
Abstract
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.File | Dimensione | Formato | |
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