QregBB {QregBB}

Implements MBB, ETBB, SMBB, and SETBB for quantile regression

Description

Implements MBB, ETBB, SMBB, and SETBB for quantile regression

Usage

QregBB(Y, X, tau, l, B = 500, h = NULL, alpha = 0.05)

Arguments

Y

the vector of response values.

X

the design matrix (including a column of ones for the intercept).

tau

the quantile of interest.

l

block size.

B

the number of Monte Carlo bootstrap samples to draw.

h

a scalar bandwidth (bandwidth matrix is h times identity).

alpha

a significance level to which the returned confidence intervals will correspond.

Value

A list is returned containing for the MBB, SMBB, ETBB, and SETBB the set of Monte Carlo draws of the pivot quantity \sqrt{n}(\hat \beta^*_n - \tilde \beta_n), confidence intervals for each component of \beta corresponding to the specified confidence level, and estimates of the asymptotic covariance matrix of the pivot quantity \sqrt{n}(\hat \beta_n - \beta).

References

#' @references

Gregory, K. B., Lahiri, S. N., & Nordman, D. J. (2018). A smooth block bootstrap for quantile regression with time series. *The Annals of Statistics*, 46(3), 1138-1166.

See Also

A 'print.QregBB' method exists which prints to the console the bootstrap standard errors for each coefficient estimator from the MBB, SMBB, ETBB, and SETBB methods as well as confidence intervals for each coefficient at the specified level.

Examples

# generate some data and perform block-bootstrap methods
n <- 100
X1 <- arima.sim(model=list(ar=c(.7,.1)),n)
X2 <- arima.sim(model=list(ar=c(.2,.1)),n)
e <- arima.sim(model=list(ar=c(.7,.1)),n)
Y <- X1 + e
X <- cbind(rep(1,n),X1,X2)

QregBB.out <- QregBB(Y,X,tau=.5,l=4,B=500,h=NULL,alpha=0.05)
QregBB.out