QTE.RD (version 1.2.0)

make.band.cq: Uniform confidence bands for conditional quantile processes

Description

make.band.cq constructs uniform confidence bands for conditional quantile processes as functions of tau for each side of the cutoff. See make.band as well. The function rdq.band calls this function to generates uniform bands for conditional quantiles.

Usage

make.band.cq(n.sam,Dc.p,Dc.m,Dr.p,Dr.m,dz,cov,taus,hh,Qy.p,Qy.m,
     bias.p,bias.m,alpha,n.sim)

Value

A list with elements:

qp

conditional quantile estimates at \(x_{0}^{+}\) (i.e., above the cutoff) without bias correction.

qp.r

bias corrected conditional quantile estimates at \(x_{0}^{+}\).

qm

conditional quantile estimates at \(x_{0}^{-}\) (i.e., below the cutoff) without bias correction.

qm.r

bias corrected conditional quantile estimates at \(x_{0}^{-}\).

ubandp

uniform confidence band for conditional quantiles at \(x_{0}^{+}\) without bias correction.

ubandp.r

uniform confidence band for conditional quantiles at \(x_{0}^{+}\) with robust bias correction.

ubandm

uniform confidence band for conditional quantiles at \(x_{0}^{-}\) without bias correction.

ubandm.r

uniform confidence band for conditional quantiles at \(x_{0}^{-}\) with robust bias correction.

sp

standard errors of the conditional quantile estimates without bias correction at \(x_{0}^{+}\).

sp.r

standard errors of the conditional quantile estimates with robust bias correction at \(x_{0}^{+}\).

sm

standard errors of the conditional quantile estimates without bias correction at \(x_{0}^{-}\).

sm.r

standard errors of the conditional quantile estimates with robust bias correction at \(x_{0}^{-}\).

Arguments

n.sam

the sample size.

Dc.p

simulated values from \(D_{1,v}(x_{0}^{+},z,\tau)\).

Dc.m

simulated values from \(D_{1,v}(x_{0}^{-},z,\tau)\).

Dr.p

simulated values from \(D_{1,v}(x_{0}^{+},z,\tau) - D_{2,v}(x_{0}^{+},z,\tau)\).

Dr.m

simulated values from \(D_{1,v}(x_{0}^{-},z,\tau) - D_{2,v}(x_{0}^{-},z,\tau)\).

dz

the number of covariates.

cov

either 0 or 1. Set cov=1 if covariates are present in the model; otherwise set cov=0.

taus

a vector of quantiles of interest.

hh

the bandwidth values.

Qy.p

estimated conditional quantiles at \((x_{0}^{+},z)\).

Qy.m

estimated conditional quantiles at \((x_{0}^{-},z)\).

bias.p

estimated bias terms at \((x_{0}^{+},z)\).

bias.m

estimated bias terms at \((x_{0}^{-},z)\).

alpha

a number between 0 and 1, the desired significance level.

n.sim

the number of simulation repetitions.

See Also

make.band

Examples

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)
tlevel2 = c(0.05,tlevel,0.95)
hh = rep(2,length(tlevel))
hh2 = rep(2,length(tlevel2))
sel = tlevel2 %in% tlevel

ab = rdq(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel2,h.tau=hh2,cov=0)
delta = c(0.05,0.09,0.14,0.17,0.19,0.17,0.14,0.09,0.05)
fp = rdq.condf(x=x,Q=ab$qp.est,bcoe=ab$bcoe.p,taus=tlevel,taul=tlevel2,delta,cov=0)
fm = rdq.condf(x=x,Q=ab$qm.est,bcoe=ab$bcoe.m,taus=tlevel,taul=tlevel2,delta,cov=0)
bp = rdq.bias(y[d==1],x[d==1],dz=0,x0=0,z0=NULL,taus=tlevel,hh,hh,fx=fp$ff[(d==1),],cov=0)
bm = rdq.bias(y[d==0],x[d==0],dz=0,x0=0,z0=NULL,taus=tlevel,hh,hh,fx=fm$ff[(d==0),],cov=0)

sa = QTE.RD:::rdq.sim(x=x,d=d,x0=0,z0=NULL,dz=0,cov=0,tt=tlevel,hh,hh,fxp=fp$ff,fxm=fm$ff,n.sim=200)
ba.cq = QTE.RD:::make.band.cq(n,Dc.p=sa$dcp,Dc.m=sa$dcm,Dr.p=sa$drp,Dr.m=sa$drm,dz=0,cov=0,
taus=tlevel,hh,Qy.p=as.matrix(ab$qp.est[sel,]),Qy.m=as.matrix(ab$qm.est[sel,]),
bias.p=bp$bias,bias.m=bm$bias,alpha=0.1,n.sim=200)