/
0_HDCQR fns.R
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0_HDCQR fns.R
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#### y: the observed variable( log(min(T,C)));
#### x: the covariates;
#### delta: the censor indicator;
#### JJ: the tau grid;
#### beta0: the initial estimator at tau0;
#### lambda: the tuning parameter
quantproc=function(y,x,delta,JJ,beta0,lambda,incr=0, tol=1e-4){
pp=dim(x)[2]; #### the number of covariates
tmpbeta=matrix(0,length(JJ),pp); #### the coefficient matrix
tmpbeta[1,]=beta0;
sto_weights=matrix(0,length(JJ),dim(x)[1]); #### stochastic weights
rproc=matrix(0,length(JJ),dim(x)[1]); #### the indictor (y>=x%*%betahat);
sto_weights[1,]=JJ[1]*2; #### the initial weight 2tau0
rproc[1,]=1*(y>=x%*%beta0); #### the initial indicator y>=x%*%betahat0;
augy1=y[which(delta==1)]; #### the observed event time
augx1=x[which(delta==1),]; #### the corresponding covariates
augx2=-apply(augx1,2,sum); #### the 2nd part in the objective function
augy=c(augy1, 1e+4, 1e+4);
for(s in 2:length(JJ)){
tuning=lambda+(s-1)*incr
Hm = H(JJ[s])-H(JJ[s-1]); #### H(tau[s])-H(tau[s-1])
sto_weights[s,]=sto_weights[s-1,]+2*Hm*rproc[s-1,]; #### update the stochastic weight for tau[s]
augx3=sto_weights[s,]%*%x; #### the 3rd part in the objective function
augx=rbind(augx1,augx2,augx3);
tmpb=coef(rq(augy~0+augx,method="lasso",tau=JJ[s],lambda=rep(tuning,pp))); #### quantile fit at tau[s];
tmpbeta[s,]=tmpb*(abs(tmpb)>=tol); #### hard threshholding;
rproc[s,] = 1*(y>x%*%tmpbeta[s,]); #### update the indicator y>=x%*%betahat at tau[s];
}
return(tmpbeta);
}
#### y: the observed variable( log(min(T,C)));
#### x: the covariates;
#### delta: the censored indicator;
#### JJ: the tau grid;
#### beta: the estimates at JJ grid
#### function to calculate the loss at quantile tau
rho=function(err,tau){
(err>0)*tau*err-(1-tau)*(err<0)*err;
}
calesterr=function(yP,xP,deltaP,JJ,beta){
fit=xP%*%t(beta);
testerr=rep(0,length(JJ));
sto_weights=matrix(0,length(JJ),dim(xP)[1]); #### stochastic weights
rproc=matrix(0,length(JJ),dim(xP)[1]); #### the indictor (y>=x%*%betahat);
sto_weights[1,]=JJ[1]; #### the initial weight 2tau0
rproc[1,]=1*(yP>=fit[,1]);
countP=(1-rproc[1,])*deltaP;
rhs=rep(JJ[1],length(countP));
testerr[1]= mean( abs(countP-rhs));
for(s in 2:length(JJ)){
Hm=H(JJ[s])-H(JJ[s-1]); #### H(tau[s])-H(tau[s-1]) ]']
sto_weights[s,]=sto_weights[s-1,]+Hm*rproc[s-1,];
rproc[s,]=1*(yP>=fit[,s]); #### update the stochastic weight for tau[s]
countP=(1-rproc[s,])*deltaP;
testerr[s]= mean(abs(countP-sto_weights[s,]));
}
return (testerr);
}
#### y: the observed variable( log(min(T,C)));
#### x: the covariates;
#### delta: the censored indicator;
#### JJ: the tau grid;
#### beta0: the initial estimator at tau0;
#### len: the length of the finer tuning parameter sequences
#### K: the K fold cross validation
rqUTlassoH_CV=function(y,x, delta, JJ, beta0,lambda, tau=0.5, len=sqrt(nrow(x)), K=5,tol=1e-4){
# the tolerance
ok<-complete.cases(x,y);
x<-x[ok,] # get rid of na's
y<-y[ok] # since regsubsets can't handle na's
pp=ncol(x);
nn=nrow(x);
x<-as.matrix(x); # in case x is not a matrix
##sto_weights=matrix(0,length(JJ),nn);
##rproc=matrix(0,length(JJ),nn);
##sto_weights[1,]=JJ[1]*2;
##rproc[1,]=1*(y>=x%*%beta0);
size <- (nn) %/% K;
rdm <- runif(nn);
ranked <- rank(rdm);
block <- (ranked-1) %/% size+1;
block <- as.factor(block);
lam=seq(lambda/2, 5*lambda, length.out=len);
cv=rep(Inf,len);
earlyStop = 0
for (i in 1: len){
ka=lam[i];
testerr=rep(0,K);
for (k in 1:K) {
yP=y[block==k]; #### the prediction response variables in k fold
xP=x[block==k,]; #### the prediction covariates matrix in k fold
deltaP=delta[block==k]; #### the prediction delta in k fold
yT=y[block!=k]; #### the test response variable in k fold
xT=x[block!=k,]; #### the test covariates matrix in k fold
deltaT=delta[block!=k]; #### the test delta in k fold
tmpbeta=quantproc(yT,xT,deltaT,JJ,beta0,ka); #### the estimates at JJ in k fold
testerr[k]=sum(calesterr(yP,xP,deltaP,JJ,tmpbeta));
}
cv[i]=sum(testerr);
#print(c(ka, cv[i]))
if (i>1 ) earlyStop = ifelse(cv[i] > cv[i-1], earlyStop+1, 0)
if (earlyStop >2) break
}
step.cv=which.min(cv);
tmpbeta=quantproc(y,x,delta,JJ,beta0,lam[step.cv]);
obj=list(beta=tmpbeta, lamb=lam[step.cv]);
return(obj);
}
rqOAH=function(y,x,tau=0.5, len=2*sqrt(nrow(x)), K=5, tol=1e-4, traceprint=FALSE){
#require(quantreg);
ok<-complete.cases(x,y);
x<-x[ok,] # get rid of na's
y<-y[ok] # since regsubsets can't handle na's
pp=ncol(x);
nn=nrow(x);
x<-as.matrix(x); # in case x is not a matrix
######## K-fold CV
size <- nn %/% K;
rdm <- runif(nn);
ranked <- rank(rdm);
block <- (ranked-1) %/% size+1;
block <- as.factor(block);
#### 1st level search (a bold search)
comp=Inf; # Cross-Validation store
count=0; #
ptr1=0; # the smallest CV
ptr2=0; # the second smallest CV
Ada=TRUE;
#ka=1/nn/2;
ka=ifelse(p<=nn, p/nn, log(p/nn));
init_lam=NULL;
init_cv=NULL;
while(Ada){
#ka=ka*2;
ka=ka*log(p);
count=count+1;
init_lam=c(init_lam,ka);
tmpb=coef(rq(y~0+x,method="lasso",tau=tau,lambda=rep(ka,pp)));
if(sum(abs(tmpb[-1]))<=tol) {Ada=FALSE;}
if (traceprint) print(c(ka, sum(abs(tmpb[-1]))))
testerr=rep(0,K);
for (k in 1:K) {
xT=x[block!=k,];
xP=x[block==k,];
yT=y[block!=k];
yP=y[block==k];
fitb=coef(rq(yT~0+xT,method="lasso",tau=tau,lambda=rep(ka,pp)));
fitb=fitb*(abs(fitb)>=tol);
err = yP-xP%*%fitb;
testerr[k]=sum((err>0)*tau*err - (1-tau)*(err<0)*err); #### why (1-tau)?
}
cv_testerr=sum(testerr);
init_cv=c(init_cv,cv_testerr);
if (cv_testerr < comp) {
comp=cv_testerr;
ptr2=ptr1;
ptr1=count;
}
}
#### 2nd search ( a finer one)
## construct a CV grid
gL=min(ptr1,ptr2); gU=max(ptr1,ptr2);
if(gL==1) {gL=2;}
gridL=max(init_lam[1], init_lam[gL-1]);
if(gU==count) {gU=count-1;}
gridU=min(init_lam[count], init_lam[gU+1]);
lam=seq(gridL, gridU,length.out=len);
cv1=rep(Inf,len);
earlyStop = 0
for (i in 1: len){
ka=lam[i];
testerr=rep(0,K);
for (k in 1:K) {
xT=x[block!=k,];
xP=x[block==k,];
yT=y[block!=k];
yP=y[block==k];
fitb=coef(rq(yT~0+xT,method="lasso",tau=tau,lambda=rep(ka,pp)));
err= yP-xP%*%fitb;
testerr[k]=sum((err>0)*tau*err-(1-tau)*(err<0)*err);
}
cv1[i]=sum(testerr);
if (traceprint) print(c(ka, cv1[i]))
if (i>1 ) earlyStop = ifelse(cv1[i] > cv1[i-1], earlyStop+1, 0)
if (earlyStop >2) break
}
step.cv1=which.min(cv1);
######## init beta by CV
betatilde=coef(rq(y~0+x,method="lasso",tau=tau,lambda=rep(lam[step.cv1],pp)));
betatilde=betatilde*(abs(betatilde)>=tol);
obj=list(beta=betatilde,lambda=lam[step.cv1]);
return(obj);
}
adquantproc=function(y,x,delta,JJ,beta0,lambda,w, tol=1e-6){
pp=dim(x)[2]; #### the number of covariates
tmpbeta=matrix(0,length(JJ),pp); #### the coefficient matrix
tmpbeta[1,]=beta0;
sto_weights=matrix(0,length(JJ),dim(x)[1]); #### stochastic weights
rproc=matrix(0,length(JJ),dim(x)[1]); #### the indictor (y>=x%*%betahat);
sto_weights[1,]=JJ[1]*2; #### the initial weight 2tau0
rproc[1,]=1*(y>=x%*%beta0); #### the initial indicator y>=x%*%betahat0;
augy1=y[which(delta==1)]; #### the observed event time
augx1=x[which(delta==1),]; #### the corresponding covariates
augx2=-apply(augx1,2,sum); #### the 2nd part in the objective function
augy=c(augy1, 1e+4, 1e+4);
ka=lambda;
for(s in 2:length(JJ)){
Hm=H(JJ[s])-H(JJ[s-1]); #### H(tau[s])-H(tau[s-1])
sto_weights[s,]=sto_weights[s-1,]+2*Hm*rproc[s-1,]; #### update the stochastic weight for tau[s]
augx3=sto_weights[s,]%*%x; #### the 3rd part in the objective function
augx=rbind(augx1,augx2,augx3);
tka=ka/length(augy);
tw=w[s,];
tw=(abs(tw)<=tka)+(2.4*tka-abs(tw))*((2.4*tka-abs(tw))>0)/((2.4-1)*tka)*(abs(tw)>tka); #SCAD weights with a=2.4
tmpb=coef(rq(augy~0+augx,method="lasso",tau=0.5,lambda=ka*tw)); #### quantile fit at tau[s];
tmpbeta[s,]=tmpb*(abs(tmpb)>=tol); #### hard threshholding;
rproc[s,]=1*(y>x%*%tmpbeta[s,]); #### update the indicator y>=x%*%betahat at tau[s];
}
return(tmpbeta);
}
rqACV=function(y,x, delta, JJ, pwei, lambda, len=sqrt(nrow(x)),K=1,tol=1e-4){
pp=ncol(x);
nn=nrow(x);
#### pointwise weights or uniform weights
if(length(pwei)==pp){
w=t(replicate(length(JJ), pwei))
} else if(length(pwei)==pp*length(JJ)){
w=pwei;
} else {
return ("invalida weights, the length of weights should be equal to # of columns of matrix or
# of quantiles times # of columns of matrix");
}
w[which(w==0)]=1e-20;
tmpbeta=matrix(0,length(JJ),pp);
##augy1=y[which(delta==1)];
##augx1=x[which(delta==1),];
##augx2=-apply(augx1,2,sum);
##augy=c(augy1, 1e+4, 1e+4);
size <- (nn) %/% K;
rdm <- runif(nn);
ranked <- rank(rdm);
block <- (ranked-1) %/% size+1;
block <- as.factor(block);
lam=seq(lambda/2, 8*lambda, length.out=len);
cv=rep(Inf,len);
earlyStop = 0
for (i in 1: len){
ka=lam[i];
testerr=rep(0,K);
sel=rep(0,dim(x)[2]);
for (k in 1:K) {
yP=y[block==k]; #### the prediction response variables in k fold
xP=x[block==k,]; #### the prediction covariates matrix in k fold
deltaP=delta[block==k]; #### the prediction delta in k fold
yT=y[block==k]; #### the test response variable in k fold
xT=x[block==k,]; #### the test covariates matrix in k fold
deltaT=delta[block==k]; #### the test delta in k fold
tka=ka/length(yT);
tw=w[1,];
tw=(abs(tw)<=tka)+(2.4*tka-abs(tw))*((2.4*tka-abs(tw))>0)/((2.4-1)*tka)*(abs(tw)>tka); #SCAD weights with a=2.4
tmpb=coef(rq(yT~0+xT,method="lasso",tau=JJ[1],lambda=ka*tw));
tmpb=tmpb*(abs(tmpb)>=tol);
tmpbeta=adquantproc(yT,xT,deltaT,JJ,tmpb,ka,w,tol=tol); #### the estimates at JJ in k fold
sel[which(apply(abs(tmpbeta),2,max)>tol)]=1;
testerr[k]=sum(calesterr(yP,xP,deltaP,JJ,tmpbeta));
}
cv[i]=sum(testerr);
if(length(which(sel==1))>nn/4) {cv[i]=1e+8;}
#print(c(ka, cv[i]))
if (i>1 ) earlyStop = ifelse(cv[i] > cv[i-1], earlyStop+1, 0)
if (earlyStop >2) break
}
step.cv=which.min(cv);
ka=lam[step.cv];
tka=ka/length(y);
tw=w[1,];
tw=(abs(tw)<=tka)+(2.4*tka-abs(tw))*((2.4*tka-abs(tw))>0)/((2.4-1)*tka)*(abs(tw)>tka); #SCAD weights with a=2.4
tmpb=coef(rq(y~0+x,method="lasso",tau=JJ[1],lambda=ka*tw));
tmpb=tmpb*(abs(tmpb)>=tol);
tmpbeta=adquantproc(y,x,delta,JJ,tmpb,lam[step.cv],w);
tmpbeta=tmpbeta*(abs(tmpbeta)>tol);
obj=list(beta=tmpbeta, lamb=lam[step.cv]);
return(obj);
}
#####################################
#
# Fused-HDCQR
#
##########################
progcombine<-function(){
count<-0
function(...) {
count<<-count+length(list(...))
setTxtProgressBar(pb,count)
utils::flush.console()
c(...)
}
}
onesplit<-function(logx,delta,zmat,J,beta0,lam1,q=sqrt(sum(delta)),thr=0.1,taus = 1:4/5){
sis <- function(logx, delta, zmat, taus = (1:8)/10, maxonly = TRUE){
crqj <- Vectorize(function(j,logx, delta, zmat, taus){
tt=crq(Surv(logx,delta,type = "right")~zmat[,j],taus=taus,method="PengHuang") ####oracle
#maxcoef <- max(abs(coef(tt, taus = taus)[2,]))
coef(tt, taus = taus)[2,]
}, vectorize.args = c("j"))
#fitcoef = crqj(1:p, taus)
fitcoef <- foreach(j = (1:p), .combine=cbind, .packages=c("MASS","quantreg","rqPen","survival")) %dopar%
crqj(j,logx, delta, zmat, taus)
#coef1 <- apply(abs(fitcoef), 2, max, na.rm=T)
coef1 <- apply(abs(fitcoef), 2, quantile, probs=0.95, na.rm=T)
rank1 <- rank(-coef1)
return(rank1)
#rank1[s1]
#list("ranks_at_taus" = SISrank, "max_rank" = rank1)
}
rqj <- function (j, logx, delta, zmat, samp1, set, taus)
{
set1<-c(j,set)
rq2 <- crq( Surv(logx[-samp1],delta[-samp1]) ~ zmat[-samp1,set1], method = "PengHuang")
as.numeric(coef(rq2,taus = taus)[2,] ) ##rq2$sol[3,temp1]
}
zmat1<-cbind(rep(1,n),zmat)
samp1<-sort(sample(n,n/2))
sampidx<-rep(0,n)
sampidx[-samp1] <- 1
#onebeta=quantproc(logx[samp1],zmat1[samp1,],delta[samp1],J,beta0,lam1) #### the estimates at JJ in k fold
#maxbeta<-apply(onebeta,2,function(a){max(abs(a))})
#coefp<-maxbeta[-1]
#q1 <- sort(abs(coefp),decreasing = T)[q]
#set = as.numeric(which(abs(coefp) > ifelse( q1 > thr, q1, thr)))
out <- sis(logx[samp1], delta[samp1], zmat[samp1,], taus = J)
#out[s1]
set = which(out <= 20)
coefall<- matrix(NA,nrow = 1+p,ncol = length(taus))
rq2 <- crq( Surv(logx[-samp1],delta[-samp1]) ~ zmat[-samp1,set], method = "PengHuang")
coefall[c(1,1+set),] <- coef(rq2,taus = taus)
tmp1 <- foreach(j = (1:p)[-set], .combine=rbind, .packages=c("MASS","glmnet","quantreg","rqPen","survival")) %dopar%
rqj(j, logx, delta, zmat, samp1, set, taus)
##stopImplicitCluster()
coefall[-c(1,1+set),] <- tmp1
return(returnlist=list("set" = set, "bhat" = coefall, "sample" = sampidx ))
}
Vsub<-function(beta,Ycount,n,n1,B, unbiased = TRUE){
v1 = (sum(cov(beta,t(Ycount))^2))*(n-1)*n/(n-n1)^2
ifelse(unbiased, v1 - n*n1/B/(n-n1)*var(beta), v1)
}
extr<-function(fit1,k,pos){
temp1<-fit1[[k]][[pos]]
}
sumfn<-function(fit1){
B = length(fit1)
BETA1<-sapply(1:B,extr,fit1=fit1,pos=2,simplify = "array")
SET1<-lapply(1:B,extr,fit1=fit1,pos=1)
Ycount<-sapply(1:B,extr,fit1=fit1,pos=3)
avgsel<- length(unlist(SET1))/B
bhat = apply((BETA1), c(1,2),mean,na.rm=T)
vbetas1<-apply(BETA1, c(1,2), Vsub,Ycount=(Ycount),n=n,n1=n/2,B=B)
sds1<- suppressWarnings(sqrt(vbetas1))
temptab<-table(unlist(SET1))
sel_freq<-rep(0,p)
sel_freq[as.numeric(names(temptab))]<-temptab/B
return(cbind(bhat,sds1,c(0,sel_freq)) )
#return(rbind(c(int,var.int,var1.int,0),cbind(bhat,sds,sds1,sel_freq)))
}
rqj <- function (j, logx, delta, zmat, samp1, set, taus)
{
set1<-c(j,set)
rq2 <- crq( Surv(logx[-samp1],delta[-samp1]) ~ zmat[-samp1,set1], method = "PengHuang")
as.numeric(coef(rq2,taus = taus)[2,] ) ##rq2$sol[3,temp1]
}
##############################
#
# MMB p-values
#
##############################
getp <- function(tmp1,set){
pmin(as.numeric(tmp1$coefficients[-1,6])*length(set), 1)
}
mb_onesplit <- function(logx,delta, zmat, q=sqrt(sum(delta)), thr=0.1){
zmat1<-cbind(rep(1,n),zmat)
samp1<-sort(sample(n,n/2))
sampidx<-rep(0,n)
sampidx[samp1]<-1
onebeta=quantproc(logx[samp1],zmat1[samp1,],delta[samp1],J,beta0,lam1) #### the estimates at JJ in k fold
maxbeta<-apply(onebeta,2,function(a){max(abs(a))})
coefp<-maxbeta[-1]
q1 <- sort(abs(coefp),decreasing = T)[q]
set = as.numeric(which(abs(coefp) > ifelse( q1 > thr, q1, thr)))
rq2 <- crq( Surv(logx[-samp1],delta[-samp1]) ~ zmat[-samp1,set], method = "PengHuang", taus = taus)
tmp1 <- summary(rq2, taus = taus, se="boot")
##tmp1[[1]]$coefficients
pmat <- matrix(1, nrow = p, ncol = length(taus))
pmat[set,]<- sapply(tmp1, getp, set=set)
return(pmat)
}
qj <- Vectorize(function(pvec, gamma = 0.05){
min(1, quantile(pvec/gamma, probs=gamma))
}, vectorize.args = "gamma")
Pj <- function(pvec, gamma_seq = .05*(1:20)){
min(1, (1-log(min(gamma_seq))))*min( qj(pvec, gamma_seq) )
}
#############################
#
# Zheng et al 2018 estimates
#
############################
zq_est <- function(logx,delta, zmat, q=sqrt(sum(delta)), thr=0.1){
zmat1<-cbind(rep(1,n),zmat)
rqbet=rqOAH(logx,zmat1,tau=tauL, K=5);
lam1 = rqbet$lambda
beta0 = rqbet$beta
print(lam1)
#tmpbeta = quantproc(logx,zmat1, delta,J,beta0,lam1);
#UW2=apply(abs(tmpbeta[-1,]),2,max);
tmp=rqUTlassoH_CV(logx,zmat1, delta, J, beta0, lam1);
betatilde_UT=tmp$beta;
lam2 <- tmp$lamb
print(lam2)
UW=apply(abs(betatilde_UT[-1,]),2,max);
tmp=rqACV(logx,zmat1, delta, J,UW,lam1);
#betahat_AUT=tmp$beta;
obj=list(beta=tmp$beta, lamb=tmp$lamb);
return(obj);
}
#------------------------------------------------------------------------#
### Compute Quantile Adaptive sure Independence Screening (QaSIS)
## for uncensored dataset
QaSIS<-function(y,x,tau)
{
p=dim(x)[2]
n=length(y)
fit<-numeric(p)
y<-y-quantile(y,tau) #centered y
x<-scale(x)
for(j in 1:p){
x0<-x[,j]
knots=quantile(x0,c(1/3,2/3))
a=bs(x0, knots=knots,degree=1)
b=rq(y~a,tau=tau)
fit[j] <-sum((b$fitted)^2)/n #avg of f^2 for each j
}
return(fit)
}
QaSIS.surv = function(x,time,delta,tau)
{
N = length(time)
p = ncol(x)
survy=survfit(Surv(time,delta)~1)
medy=survy$time[min(which(survy$surv<tau))]
survc=survfit(Surv(time,1-delta)~1)
wt=rep(0,N)
for(i in 1:N)
{
k=max(which(round(survc$time,4)<=round(time[i],4)))
wt[i]=delta[i]/survc$surv[k]
}
fit=numeric(p)
for(k in 1:p)
{
pix=bs(x[,k],df=3)
betac=rq(time~pix, tau=tau, weight=wt)
fit[k]=mean((predict(betac)-medy)^2)
}
return(fit)
}
##### functions for QA-SIS and SIS
maxwhich <- Vectorize(function(a, vec){
max(which(vec<= a))
}, vectorize.args = c("a"))
minwhich <- Vectorize(function(a, vec){
idx = ifelse(min(which(vec< a)) == Inf, length(vec), min(which(vec< a)) )
}, vectorize.args = c("a"))
fitj <- Vectorize(function(j,taus,wt, medy, sp = FALSE){
if(sp) pix = bs(zmat[,j],df=3)
else pix = zmat[,j]
betac=try(rq(logx~pix, tau=taus, weight=wt))
#if (length(betac) > 1)
rowMeans((t(predict(betac)) - medy)^2 )
}, vectorize.args = c("j"))
qasis <- function(logx, delta, zmat, taus = (1:8)/10, sp=TRUE){
survy=survfit(Surv(logx,delta)~1)
medy=survy$time[minwhich(taus, survy$surv)]
survc=survfit(Surv(logx,1-delta)~1)
kvec <- maxwhich(logx, survc$time)
wt = delta/survc$surv[kvec]
fit= fitj(1:p, taus, wt, medy, sp=sp)
#QA_rank <- apply(fit, 1, order, decreasing = TRUE)
colnames(fit) <- 1:p
rownames(fit) <- round(taus,3)
return(fit)
}
########################
#
# Fan et al 2009 SIS
#
###############################
crqj <- Vectorize(function(j,taus){
tt=crq(Surv(logx,delta,type = "right")~zmat[,j],taus=taus,method="PengHuang") ####oracle
#maxcoef <- max(abs(coef(tt, taus = taus)[2,]))
coef(tt, taus = taus)[2,]
}, vectorize.args = c("j"))
sis <- function(logx, delta, zmat, taus = (1:8)/10, maxonly = TRUE){
fitcoef = crqj(1:p, taus)
#coef1 <- apply(abs(fitcoef), 2, max, na.rm=T)
coef1 <- apply(abs(fitcoef), 2, quantile, probs=0.95, na.rm=T)
#SISrank <- apply(abs(fitcoef), 1, order, decreasing = TRUE)
#SISrank <- apply(-abs(fitcoef), 1, rank)
#colnames(SISrank) <- round(taus,3)
#rownames(SISrank) <- 1:p
#SISrank[s1,]
rank1 <- rank(-coef1)
return(rank1)
#rank1[s1]
#list("ranks_at_taus" = SISrank, "max_rank" = rank1)
}
##############################
#
# Define phi functions
#
##############################
a=48;
b=3;
devfunc=function(x) {
1/dnorm(qnorm(x))-a*(2*x-1);
}
cross.x=uniroot(devfunc, c(0.5, 0.9))$root;
dy=qnorm(cross.x)-a*(cross.x-1/2)^2
c.1=1/dnorm(qnorm(0.9));
d.1=qnorm(0.9)-dy-0.9*c.1;
c.2=1/dnorm(qnorm(0.1));
d.2=qnorm(0.1)+dy-0.1*c.2;
qnapprox.1=function(x) {
1*(b*((a*(x-1/2)^2)*as.numeric(x<cross.x&x>0.5)+(qnorm(pmin(x, 0.9))-dy)*as.numeric(x>=cross.x&x<0.9)+(c.1*x+d.1)*as.numeric(x>=0.9)));
}
qnapprox.2=function(x) {
1*(b*((-a*(x-1/2)^2)*as.numeric(x>(1-cross.x)&x<0.5)+(qnorm(pmax(x, 0.1))+dy)*as.numeric(x<=(1-cross.x)&x>0.1)+(c.2*x+d.2)*as.numeric(x<=0.1)));
}
qeffect.1=function(x) {
qnapprox.1(x+0.05);
}
qeffect.2=function(x) {
qnapprox.2(x-0.05);
}
H<-function(x){
return (-log(1-x));
}