| 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 |
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 |
... |
other arguments to be passed to |
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)