quantreg (version 3.52)

khmaladze.test: 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,'' Theory of Prob. and its Apps, 26, 240--257.

Koenker, Roger and Zhijie Xiao (2000), "Inference on the Quantile Regression Process'', 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))
khmaladze.test(fit, nullH = "location")