# critval

##### Hotelling Critical Values

Critical values for uniform confidence bands for rqss fitting

- Keywords
- regression

##### Usage

`critval(kappa, alpha = 0.05, rdf = 0)`

##### Arguments

- kappa
length of the tube

- alpha
desired non-coverage of the band, intended coverage is 1 - alpha

- rdf
"residual" degrees of freedom of the fitted object. If

`rdf=0`

then the Gaussian version of the critical value is computed, otherwise the value is based on standard Student t theory.

##### Details

The Hotelling tube approach to inference has a long and illustrious history. See Johansen and Johnstone (1989) for an overview. The implementation here is based on Sun and Loader (1994) and Loader's locfit package, although a simpler root finding approach is substituted for the iterative method used there. At this stage, only univariate bands may be constructed.

##### Value

A scalar critical value that acts as a multiplier for the uniform confidence band construction.

##### References

Hotelling, H. (1939): ``Tubes and Spheres in $n$-spaces, and a class
of statistical problems,'' *Am J. Math*, 61, 440--460.

Johansen, S., I.M. Johnstone (1990): ``Hotelling's
Theorem on the Volume of Tubes: Some Illustrations in Simultaneous
Inference and Data Analysis,'' *The Annals of Statistics*, 18, 652--684.

Sun, J. and C.V. Loader: (1994) ``Simultaneous Confidence Bands for Linear Regression
and smoothing,'' *The Annals of Statistics*, 22, 1328--1345.

##### See Also

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