li_powell: Asymmetric-Laplace-type Working Likelihood For Cenaored Quantile Regression
Description
Asymmetric-Laplace-type working likelihood for linear
quantile regression with responses
subject to left censoring at zero
Usage
li_powell(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-type) likelihood function (the part involving the regression coefficients)
Details
The asymmetric-Laplace-type working likelihood is proportional to exponential
of the negative Powell objective function for censored quantile regression
References
Powell, J. L. (1986). Censored regression quantiles. Journal of Econometrics, 32, 143-155.
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.