PTQTE.Khmaladze.fit {RATest}

Quantile-Based Permutation Test with an Estimated Nuisance Parameter

Description

A permutation test for testing whether the quantile treatment effects are constant across quantiles. The permutation test considered here is based on the Khmaladze transformation of the quantile process (Koenler and Xiao (2002)), and adapted by Chung and Olivares (2021).

Usage

PTQTE.Khmaladze.fit(
  Y,
  Z,
  taus = seq(0.1, 0.9, by = 0.05),
  alpha = 0.05,
  n.perm = 999
)

Arguments

Y

Numeric. Vector of responses.

Z

Numeric. Treatment indicator. Z=1 if the unit is in the treatment group, and Z=0 if the unit is in the control group.

taus

quantiles at which the process is to be evaluated, if any of the taus lie outside (0,1) then the full process is computed for all distinct solutions.

alpha

Significance level.

n.perm

Numeric. Number of permutations needed for the stochastic approximation of the p-values. The default is n.perm=999.

Value

An object of class "PTQTE.Khmaladze" containing at least the following components:

n_populations

Number of grups.

N

Sample Size.

KS.obs

Observed two-sample Kolmogorov-Smirnov test statistic based on the quantile process.

shift

The estimated nuisance parameter.

rej.rule

Binary decision for the permutation test, where 1 means rejection.

pvalue

P-value.

KS.perm

Vector. Test statistic recalculated for all permutations used in the stochastic approximation.

n_perm

Number of permutations.

sample_sizes

Groups size.

Author(s)

Maurcio Olivares

References

Khmaladze, E. (1981). Martingale Approach in the Theory of Goodness-of-fit Tests. Theory of Probability and its Application, 26: 240–257. Koenker, R. and Xiao, Z. (2002) Inference on the Quantile Regression Process. Econometrica, 70(4): 1583-1612. Chung, E. and Olivares, M. (2021). Comment on "Can Variation in Subgroups' Average Treatment Effects Explain Treatment Effect Heterogeneity? Evidence from a Social Experiment."

Examples

## Not run: 
dta <- data.frame(Y=rnorm(100),Z=sample(c(0,1), 100, replace = TRUE))
pt.QTE<-PTQTE.Khmaladze.fit(dta$Y,dta$Z,taus=seq(.1,.9,by=0.05),alpha=0.05,n.perm = 499)
summary(pt.QTE)

## End(Not run)