## Description

Bayesian quantile regression based on asymmetric Laplace likelihood with posterior variance adjustment

## Usage

 ```1 2``` ```BQR(y, x, tau, niter = 20000, burn_in = 4000, prop_cov = NULL, level = 0.9) ```

## Arguments

 `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

## Details

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.

## Value

A list of the following commponents is returned

estpar: posterior mean of the regression coefficient vector

PSD: posterior standard deviation without adjustment

sig: estimated scale parameter

MCMCsize: effective size of the chain

## 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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```#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) ```

### Example output

```Loading required package: quantreg

Attaching package: 'SparseM'

The following object is masked from 'package:base':

backsolve

Attaching package: 'survival'

The following object is masked from 'package:quantreg':

untangle.specials

\$estpar
[1] -0.06855049  1.99545736  1.97272196

\$PSD
[1] 0.08616764 0.07904206 0.09566932

[1] 0.09914312 0.07985734 0.11146693

\$CI.BAL
LB         UB
[1,] -0.2102836 0.07318266
[2,]  1.8654447 2.12546999
[3,]  1.8153599 2.13008398

LB         UB
[1,] -0.2316264 0.09452543
[2,]  1.8641037 2.12681100
[3,]  1.7893752 2.15606874

\$sig
[1] 0.5300029

\$MCMCsize
var1     var2     var3
1308.693 1293.016 1290.231
```

AdjBQR documentation built on May 1, 2019, 10:26 p.m.