AdjBQR (version 1.0)

li_reg: Asymmetric Laplace Working Likelihood For Linear Quantile Regression

Description

Asymmetric Laplace Working Likelihood For Linear Quantile Regression

Usage

li_reg(pars, y, x, tau, sig)

Arguments

pars

regression coefficient vector

y

the response vector

x

the design matrix with one in the first column corresponding to the intercept

tau

the quantile level

sig

scale parameter sigma

Value

the working log (asymmetric Laplace) likelihood function (the part involving the regression coefficients)

Details

The asymmetric Laplace working likelihood is proportional to exponential of the negative quantile objective function for linear quantile regression

References

Yang, Y., Wang, H. and He, X. (2015). Posterior inference in Bayesian quantile regression with asymmetric Laplace likelihood. International Statistical Review, 2015. doi: 10.1111/insr.12114.