# summary.crq

##### Summary methods for Censored Quantile Regression

Returns a summary object for a censored quantile regression fit. A null value will be returned if printing is invoked.

- Keywords
- regression

##### Usage

```
# 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, ...)
```

##### Arguments

- object
An object of class

`"crq"`

produced by a call to`crq()`

.- taus
Quantiles to be summarized. Specifying only one value can produce annoying error messages harmful to your mental health.

- x
An object of class

`"crq"`

produced by a call to`crq()`

.- se
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.- covariance
logical flag to indicate whether the full covariance matrix of the estimated parameters should be returned.

- nrow
Number of rows of the plot layout.

- ncol
Number of columns of the plot layout.

- alpha
Confidence level for summary intervals.

- digits
Number of digits to be printed in summary display.

- CoxPHit
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`

##### Details

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.

##### Value

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

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.

##### References

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.

##### See Also

*Documentation reproduced from package quantreg, version 5.54, License: GPL (>= 2)*