p-values from proc quantreg

[sparsityBlues]

in proc quantreg, what is the difference between the p-values in the quantile parameter estimate tables and the p-values from the "TEST" statement tables for a single variable?

my code is:

proc quantreg data= have alpha=0.1 ci=resampling algorithm=interior(tolerance=5.e-4);
class block sex race;
model ln_iss = month age_v2 block sex race/ quantile= 0.1 0.3 0.5 0.7 0.9 ;
test block / wald lr qinteract;
test sex / wald lr qinteract;
test age_v2 / wald lr qinteract;
test race / wald lr qinteract;
format block blockfmt. ;
run;

each quantile  parameter estimate table gives a p-value for each co-variate. a second p-value for each variable is output from the "test" statement. are both testing the same thing?

from the documentation for sas 9.4:

Three tests are available in the QUANTREG procedure for the linear null hypothesis that beta2=0 at the quantile tau.

what is the null hypothesis in the parameter estimate tables? are these different statistical test of the same null hypothesis?

[Rick_SAS · Accepted solution]

> each quantile parameter estimate table gives a p-value for each co-variate. a second p-value for each variable is output from the "test" statement. are both testing the same thing?

Yes, both are testing the null hypothesis that the regression coefficient for the given quantile is zero. You will get one p-value for each coefficient.

> what is the null hypothesis in the parameter estimate tables? are these different statistical test of the same null hypothesis?

Yes, different tests. Since you specified CI=RESAMPLING, the p-values in the ParameterEstimates table are estimated by using a resampling (bootstrap) method. See the doc for the CI= option.

For the TEST statements, the tables show the estimates from the Wald and LR tests, as described in the doc. 

The QINTERACT option performs a different test. The table titled "Test Results Equal Coefficients
Across Quantiles" shows the test statistics for the test that the coefficients do not depend on the quantiles. In other words, the regression line for each quantile has a common slope.

[sparsityBlues]

super, thanks--i'm just learning quantreg so just wanted to be sure i was interpreting everything correctly.