Package 'QregBB'

Block Bootstrap Methods for Quantile Regression in Time Series

Description

Implements moving-blocks bootstrap and extended tapered-blocks bootstrap, as well as smooth versions of each, for quantile regression in time series. This package accompanies the paper: 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.

Details

Implements moving-blocks bootstrap and extended tapered-blocks bootstrap, as well as smooth versions of each, for quantile regression in time series. This package accompanies Gregory et al. (2018).

Package:	QregBB
Type:	Package
Title:	Block Bootstrap Methods for Quantile Regression in Time Series
Version:	1.0.0
Date:	2022-06-01
Author:	Karl Gregory
Maintainer:	Karl Gregory <[email protected]>
Description:	Implements moving-blocks bootstrap and extended tapered-blocks bootstrap, as well as smooth versions of each, for quantile regression in time series. This package accompanies the paper: 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.
License:	GPL-3
RoxygenNote:	7.2.0
Imports:	quantreg
Repository:	https://gregorkb.r-universe.dev
RemoteUrl:	https://github.com/gregorkb/qregbb
RemoteRef:	HEAD
RemoteSha:	db3656c4ace07208e3f7fbad6005908f3630400f

Index of help topics:

QregBB                  Implements MBB, ETBB, SMBB, and SETBB for
                        quantile regression
QregBB-package          Block Bootstrap Methods for Quantile Regression
                        in Time Series
getNPPIblksizesQR       Chooses block sizes for MBB, ETBB, SMBB, and
                        SETBB via the NPPI for quantile regression

The main function is the QregBB function, which implements the moving-blocks bootstrap (MBB), the extended tapered-blocks bootstrap (ETBB), and smooth versions of each (SMBB, SETBB). The function getNPPIblksizesQR chooses the block size based on the non-parametric plug-in method described in Lahiri (2013). For the smooth methods, the bandwidth is chosen by using the function bw.SJ function on the fitted residuals; then the bandwidth matrix is the identity matrix times the value returned by bw.SJ.

Author(s)

Karl Gregory

Maintainer: Karl Gregory <[email protected]>

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.

Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer, New York.

Examples

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

---

Chooses block sizes for MBB, ETBB, SMBB, and SETBB via the NPPI for quantile regression

Description

Chooses block sizes for MBB, ETBB, SMBB, and SETBB via the NPPI for quantile regression

Usage

getNPPIblksizesQR(Y, X, tau, min.in.JAB = 100)

Arguments

Y	the vector of response values.
X	the design matrix (including a column of ones for the intercept).
tau	the quantile of interest.
min.in.JAB	the minimum number of Monte-Carlos draws desired in each jackknife draw

Details

This function is based on the nonparametric plug-in (NPPI) method discussed in Lahiri (2003), which makes use of the jackknife-after-bootstrap (JAB).

Value

Returns a list of the NPPI-selected block sizes for the MBB, SMBB, ETBB, and SETBB.

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.

Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer, New York.

Examples

# generate some data and use NPPI to choose block sizes for MBB, SMBB, ETBB, and SETBB.
n <- 50
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)

blksize.out <- getNPPIblksizesQR(Y,X,tau=.5)
blksize.out

---

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

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