Returns a summary object for a censored quantile regression fit. A null value will be returned if printing is invoked.
# S3 method for crq
summary(object, taus = 1:4/5, alpha = .05, se="boot", covariance=TRUE, ...)
# S3 method for summary.crq
print(x, digits = max(5, .Options$digits - 2), ...)
# S3 method for summary.crqs
print(x, ...)
# S3 method for summary.crqs
plot(x, nrow = 3, ncol = 3, CoxPHit = NULL, ...)For method "Powell" an object of class summary.crq is returned
with the following components:
a p by 4 matrix consisting of the coefficients, their estimated standard errors, their t-statistics, and their associated p-values.
the estimated covariance matrix for the coefficients in the model,
provided that covariance = TRUE appears in the calling sequence.
the residual degrees of freedom
the quantile estimated
For the other methods an object of class summary.crq is returned
with the following components:
a list of p by 6 matrix consisting of the coefficients, upper and lower bounds
for a (1-alpha) level confidence interval, their estimated standard
errors, their t-statistics, and their associated p-values, one component for each
element of the specified taus vector.
the estimated covariance matrix for the coefficients in the model,
provided that covariance = TRUE in the called sequence.
An object of class "crq" produced by a call to crq().
Quantiles to be summarized. This should be a vector of length greater than one.
An object of class "crq" produced by a call to crq().
specifies the method used to compute standard standard errors. but
the only available method (so far) is "boot". Further arguments to
boot.crq and boot.rq can be passed with
the ... argument.
logical flag to indicate whether the full covariance matrix of the estimated parameters should be returned.
Number of rows of the plot layout.
Number of columns of the plot layout.
Confidence level for summary intervals.
Number of digits to be printed in summary display.
An object of class coxph produced by coxph.
Optional arguments to summary, e.g. to specify bootstrap methods
sample sizes, etc. see boot.rq and boot.crq
For the Powell method the resampling strategy used by the
se = "boot" method is based on the Bilias, Chen and Ying (2000)
proposal. For the Portnoy and Peng-Huang methods the bootstrapping
is by default actually based on a delete-d jackknife, as described in
Portnoy (2013), but resampling xy pairs using either conventional multinomial
resampling or using exponential weighting as in Bose and Chatterjee (2003)
can be used by specifying the bmethod argument. Note that the default
number of replications is set at \(R = 100\) a value that is obviously too small for
most applications. This is done merely to speed up the examples in the
documentation and facilitate testing. Larger, more appropriate values of \(R\)
can be passed to the bootstrapping functions via the ... argument
of the summary method. It is important to recognize that when some
of the bootstrap replications are NA they are simply ignored in the computation
of the confidence bands and standard errors as currently reported. The number
of these NAs is returned as part of the summary.crq object, and
when printed is also reported.
Bose, A. and S. Chatterjee, (2003) Generalized bootstrap for estimators of minimizers of convex functions, J. Stat. Planning and Inf, 117, 225-239.
Bilias, Y. Chen, S. and Z. Ying, (2000) Simple resampling methods for censored quantile regression, J. of Econometrics, 99, 373-386.
Portnoy, S. (2013) The Jackknife's Edge: Inference for Censored Quantile Regression, CSDA, forthcoming.
crq, QTECox