# KhmaladzeTest

##### Tests of Location and Location Scale Shift Hypotheses for Linear Models

Tests of the hypothesis that a linear model specification is of the location shift or location-scale shift form. The tests are based on the Doob-Meyer Martingale transformation approach proposed by Khmaladze(1981) for general goodness of fit problems as adapted to quantile regression by Koenker and Xiao (2002).

- Keywords
- htest

##### Usage

```
KhmaladzeTest(formula, data = NULL, taus = 1:99/100, nullH = "location" ,
trim = c(0.05, 0.95), h = 1, ...)
```

##### Arguments

- formula
a formula specifying the model to fit by

`rqProcess`

- data
a data frame within which to interpret the formula

- taus
An equally spaced grid of points on which to evaluate the quantile regression process, if any taus fall outside (0,1) then the full process is computed.

- nullH
a character vector indicating whether the "location" shift hypothesis (default) or the "location-scale" 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).

- h
an initial bandwidth for the call to

`akj`

.- ...
other arguments to be passed to

`summary.rq.`

##### Value

an object of class KhmaladzeTest is returned containing:

The form of the null hypothesis.

Joint test statistic of the hypothesis that all the slope parameters of the model satisfy the hypothesis.

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,'' *Theory of Prob. and its Apps*, 26,
240--257.

Koenker, Roger and Zhijie Xiao (2002), ``Inference on the Quantile
Regression Process'', *Econometrica*, 81, 1583--1612.
http://www.econ.uiuc.edu/~roger/research/inference/inference.html

##### Examples

```
# NOT RUN {
data(barro)
T = KhmaladzeTest( y.net ~ lgdp2 + fse2 + gedy2 + Iy2 + gcony2,
data = barro, taus = seq(.05,.95,by = .01))
plot(T)
# }
```

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