BQR {AdjBQR} | R Documentation |
Bayesian quantile regression based on asymmetric Laplace likelihood with posterior variance adjustment
BQR(y, x, tau, niter = 20000, burn_in = 4000, prop_cov = NULL, level = 0.9)
y |
the response vector |
x |
the design matrix. If the first column of x is not all ones, a column of ones will be added. |
tau |
the quantile level of interest |
niter |
integer: number of iterations to run the chain for. Default 20000. |
burn_in |
integer: discard the first burn_in values. Default 100. |
prop_cov |
covariance matrix giving the covariance of the proposal distribution. This matrix need not be positive definite. If the covariance structure of the target distribution is known (approximately), it can be given here. If not given, the diagonal will be estimated via the Fisher information matrix. |
level |
nominal confidence level for the credible interval |
The function returns the unadjusted and adjusted posterior standard deviation, and unadjusted and adjusted credible intervals for Bayesian quantile regression based on asymmetric Laplace working likelihood.
A list of the following commponents is returned
estpar: posterior mean of the regression coefficient vector
PSD: posterior standard deviation without adjustment
PSD.adj: posterior standard deviation with adjustment
CI.BAL: credible interval without adjustment
CI.BAL.adj: credible interval with adjustment
sig: estimated scale parameter
MCMCsize: effective size of the chain
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.
#A simulation example library(AdjBQR) n=200 set.seed(12368819) x1 = rnorm(n) x2 = rnorm(n) y=2*x1+2*x2+rt(n,df=3) x = cbind(1, x1, x2) ## Bayesian quantile regression based on asymmetric Laplace likelihood BQR(y, x, tau=0.5, level=0.9)