## Tests of Location and Location Scale Hypothesis for Linear Models

### Description

Tests of the hypothesis that a linear model specification is of the location and location-scale shift form. The tests are based on the Doob-Meyer transformation approach proposed by Khmaladze(1981) for general goodness of fit problems, and adapted to quantile regression by Koenker and Xiao (2001).

### Usage

```khmaladze.test( fit, nullH = "location-scale" ,  trim = c(0.25, 0.75) )
```

### Arguments

 `fit` an object produced by `rqProcess` containing components describing the quantile regression process for the model. `nullH` a character vector indicating whether the "location-scale" shift hypothesis (default) or the "location" shift hypothesis should be tested. `trim` a vector indicating the lower and upper bound of the quantiles to included in the computation of the test statistics (only, not estimates). This might be required due to tail behavior.

### Value

an object of class khmaladze is returned containing:

 `nullH` The form of the null hypothesis. `Tn` Joint test statistic of the hypothesis that all the slope parameters of the model satisfy the hypothesis. `THn` Vector of test statistics testing whether individual slope parameters satisfy the null hypothesis.

### References

Khmaladze, E. (1981) ``Martingale Approach in the Theory of Goodness-of-fit Tests,'' textit{Theory of Prob. and its Apps}, 26, 240–257.

Koenker, Roger and Zhijie Xiao (2000), "Inference on the Quantile Regression Process'', textit{Econometrica}, 81, 1583–1612. http://www.econ.uiuc.edu/~roger/research/inference/inference.html

### Examples

```data(barro)
fit <- rqProcess( y.net ~ lgdp2 + fse2 + gedy2 + Iy2 + gcony2,
data = barro, taus = seq(.1,.9,by = .05))