make.band.cq {QTE.RD}

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)

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.

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}^{-}.

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 = 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 = 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)