quantreg: KhmaladzeTest – R documentation

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KhmaladzeTest

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)

quantreg

Quantile Regression

v5.85

GPL (>= 2)

Authors

Roger Koenker [cre, aut], Stephen Portnoy [ctb] (Contributions to Censored QR code), Pin Tian Ng [ctb] (Contributions to Sparse QR code), Blaise Melly [ctb] (Contributions to preprocessing code), Achim Zeileis [ctb] (Contributions to dynrq code essentially identical to his dynlm code), Philip Grosjean [ctb] (Contributions to nlrq code), Cleve Moler [ctb] (author of several linpack routines), Yousef Saad [ctb] (author of sparskit2), Victor Chernozhukov [ctb] (contributions to extreme value inference code), Ivan Fernandez-Val [ctb] (contributions to extreme value inference code), Brian D Ripley [trl, ctb] (Initial (2001) R port from S (to my everlasting shame -- how could I have been so slow to adopt R!) and for numerous other suggestions and useful advice)

Initial release