Uniform confidence band for QTE.

summary.qte returns uniform confidence bands and standard errors for QTE estimates.

Usage

# S3 method for class 'qte'
summary(object, alpha = 0.1, ...)

Arguments

object

It is an object of class "qte" produced by rd.qte.

alpha

a number between 0 and 1, the desired significance level. For example, setting alpha = 0.1 yields a 90% uniform confidence band. Multiple significance levels can be specified, e.g., alpha = c(0.1, 0.05).

...

optional arguments.

Value

A list with elements:

qte

QTE estimates.

uband

uniform confidence band for QTE. If bias=1, the band is robust capturing the effect of the bias correction. If bias=0, no bias correction is implemented.

sigma

standard errors for each quantile level. If bias=1, its value captures the effect of the bias correction. If bias=0, no bias correction is implemented.

qp.est

conditional quantile estimates on the right side of \(x_{0}\) (or for the \(D=1\) group).

qm.est

conditional quantile estimates on the left side of \(x_{0}\) (or for the \(D=0\) group).

uband.p

uniform confidence band for conditional quantiles on the right side of \(x_{0}\).

uband.m

uniform confidence band for conditional quantiles on the left side of \(x_{0}\).

References

Zhongjun Qu, Jungmo Yoon, Pierre Perron (2024), "Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits," The Review of Economics and Statistics; doi:10.1162/rest_a_01168

Zhongjun Qu and Jungmo Yoon (2019), "Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs," Journal of Business and Economic Statistics, 37(4), 625–647; doi:10.1080/07350015.2017.1407323

Examples

# Without covariate
n <- 500
x <- runif(n,min=-4,max=4)
d <- (x > 0)
y <- x + 0.3*(x^2) - 0.1*(x^3) + 1.5*d + rnorm(n)
tlevel = seq(0.1,0.9,by=0.1)
A <- rd.qte(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,bdw=2,bias=1)
A2 <- summary(A,alpha=0.1)

# (continued) With covariates
z <- sample(c(0,1),n,replace=TRUE)
y <- x + 0.3*(x^2) - 0.1*(x^3) + 1.5*d + d*z + rnorm(n)
A <- rd.qte(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),tau=tlevel,bdw=2,bias=1)
A2 <- summary(A,alpha=0.1)