# boot.crq

0th

Percentile

##### Bootstrapping Censored Quantile Regression

Functions used to estimated standard errors, confidence intervals and tests of hypotheses for censored quantile regression models using the Portnoy and Peng-Huang methods.

Keywords
regression
##### Usage
boot.crq(x, y, c, taus, method, ctype = "right", R = 100, mboot, bmethod = "jack", ...)
##### Arguments
x

The regression design matrix

y

The regression response vector

c

The censoring indicator

taus

The quantiles of interest

method

The fitting method: either "P" for Portnoy or "PH" for Peng and Huang.

ctype

Either "right" or "left"

R

The number of bootstrap replications

bmethod

The bootstrap method to be employed. There are (as yet) three options: method = "jack" uses the delete-d jackknife method described by Portnoy (2013), method = "xy-pair" uses the xy-pair method, that is the usual multinomial resampling of xy-pairs, while method = "Bose" uses the Bose and Chatterjee (2003) weighted resampling method with exponential weights. The "jack" method is now the default.

mboot

optional argument for the bootstrap method: for bmethod = "jack" it specifies the number, d, of the delete-d jackknife, for method = "xy-pair" it specifies the size of the bootstrap samples, that permits subsampling (m out of n) bootstrap. By default in the former case it is set to 2 [sqrt(n)], for the latter the default is n. Obviously mboot should be substantially larger than the column dimension of x, and should be less than the sample size in both cases.

...

Optional further arguments to control bootstrapping

##### Details

There are several refinements that are still unimplemented. Percentile methods should be incorporated, and extensions of the methods to be used in anova.rq should be made. Note that bootstrapping for the Powell method "Powell" is done via boot.rq. For problems with n > 3000 a message is printed indicated progress in the resampling.

##### Value

A matrix of dimension R by p is returned with the R resampled estimates of the vector of quantile regression parameters. When mofn < n for the "xy" method this matrix has been deflated by the factor sqrt(m/n)

##### References

Bose, A. and S. Chatterjee, (2003) Generalized bootstrap for estimators of minimizers of convex functions, J. Stat. Planning and Inf, 117, 225-239. Portnoy, S. (2013) The Jackknife's Edge: Inference for Censored Quantile Regression, CSDA, forthcoming.

summary.crq