R: Tests of Location and Location Scale Shift Hypotheses for...

KhmaladzeTest {quantreg} | R Documentation

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

### Description

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).

### 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:

`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,” 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

    data(barro)
    T = KhmaladzeTest( y.net ~ lgdp2 + fse2 + gedy2 + Iy2 + gcony2,
    		data = barro, taus = seq(.05,.95,by = .01))
    plot(T)

[Package quantreg version 5.70 Index]