Functions used to estimated standard errors, confidence intervals and tests of hypotheses for censored quantile regression models using the Portnoy and Peng-Huang methods.
boot.crq(x, y, c, taus, method, ctype = "right", R = 100, mboot, bmethod = "jack", ...)The regression design matrix
The regression response vector
The censoring indicator
The quantiles of interest
The fitting method: either "P" for Portnoy or "PH" for Peng and Huang.
Either "right" or "left"
The number of bootstrap replications
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.
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
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)
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.
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.