Nothing
intraBeta=function(d,n,Quantile=0.999,B=0,DB=c(0,0),JC=FALSE,CI_Boot,type="bca", plot=FALSE){
if(is.numeric(d)){d=d}else{stop("d is not numeric")}
if(is.numeric(n)){n=n}else{stop("n is not numeric")}
if(B==0&& plot==TRUE){stop("please select a number of bootstrap repititions for the plot")}
if(B%%1==0){B=B}else{stop("B is not an integer")}
if(DB[1]%%1==0 && DB[2]%%1==0 ){DB=DB}else{stop("At least one entry in DB is not an integer")}
if(length(d)==length(n)){}else{stop("Input vectors do not have the same length")}
d1=d/n
estimate=function(d1){
PD=mean(d1)
alpha=PD*((PD*(1-PD))/var(d1)-1)
beta=alpha/PD*(1-PD)
foo=function(rho){
Var_Beta=qbeta(Quantile, alpha, beta)
Var_Vasicek=pnorm((qnorm(PD)+sqrt(rho)*qnorm(Quantile))/sqrt(1-rho))
return(abs(Var_Beta-Var_Vasicek))
}
Est<-list(Original =optimise(foo, interval = c(0, 1), maximum = FALSE)$minimum)
}
Estimate_Standard<-estimate(d1)
if(B>0){
N<-length(n)
D<- matrix(ncol=1, nrow=N,d1)
BCA=function(data, indices){
d <- data[indices,]
tryCatch(estimate(d)$Original,error=function(e)NA)
}
boot1<- boot(data = D, statistic = BCA, R=B)
Estimate_Bootstrap<-list(Original = boot1$t0, Bootstrap=2*boot1$t0 - mean(boot1$t,na.rm = TRUE),bValues=boot1$t )
if(missing(CI_Boot)){Estimate_Bootstrap=Estimate_Bootstrap}else{
if(type=="norm"){Conf=(boot.ci(boot1,conf=CI_Boot,type = type)$normal[2:3])}
if(type=="basic"){Conf=(boot.ci(boot1,conf=CI_Boot,type = type)$basic[4:5])}
if(type=="perc"){Conf=(boot.ci(boot1,conf=CI_Boot,type = type))$percent[4:5]}
if(type=="bca"){Conf=(boot.ci(boot1,conf=CI_Boot,type = type))$bca[4:5]}
if(type=="all"){Conf=(boot.ci(boot1,conf=CI_Boot,type = type))}
Estimate_Bootstrap<-list(Original = boot1$t0, Bootstrap=2*boot1$t0 - mean(boot1$t,na.rm = TRUE),CI_Boot=Conf,bValues=boot1$t )
}
if(plot==TRUE){
Dens<-density(boot1$t, na.rm = TRUE)
XY<-cbind(Dens$x,Dens$y)
label<-data.frame(rep("Bootstrap density",times=length(Dens$x)))
Plot<-cbind(XY,label)
colnames(Plot)<-c("Estimate","Density","Label")
SD<-cbind(rep(boot1$t0,times=length(Dens$x)), Dens$y,rep("Standard estimate",times=length(Dens$x)))
colnames(SD)<-c("Estimate","Density","Label")
BC<-cbind(rep(Estimate_Bootstrap$Bootstrap,times=length(Dens$x)), Dens$y,rep("Bootstrap corrected estimate",times=length(Dens$x)))
colnames(BC)<-c("Estimate","Density","Label")
Plot<-rbind(Plot,SD, BC)
Plot$Estimate<-as.numeric(Plot$Estimate)
Plot$Density<- as.numeric(Plot$Density)
Estimate<-Plot$Estimate
Density<-Plot$Density
Label<-Plot$Label
P<-ggplot()
P<-P+with(Plot, aes(x=Estimate, y=Density, colour=Label)) +
geom_line()+
scale_colour_manual(values = c("black", "red", "orange"))+
theme_minimal(base_size = 15) +
ggtitle("Bootstrap Density" )+
theme(plot.title = element_text(hjust = 0.5),legend.position="bottom",legend.text = element_text(size = 12),legend.title = element_text( size = 12), legend.justification = "center",axis.text.x= element_text(face = "bold", size = 12))
print(P)
}
}
if(DB[1]!=0){
IN=DB[1]
OUT=DB[2]
theta1=NULL
theta2=matrix(ncol = OUT, nrow=IN)
for(i in 1:OUT){
N<-length(d1)
Ib<-sample(N,N,replace=TRUE) ## sampling with replacement
Db<-d1[Ib]
try(theta1[i]<-estimate(Db)$Original, silent = TRUE)
for(c in 1:IN){
Ic<-sample(N,N,replace=TRUE) ## sampling with replacement
Dc<-Db[Ic]
try( theta2[c,i]<-estimate(Dc)$Original, silent = TRUE)
}
}
Boot1<- mean(theta1, na.rm = TRUE)
Boot2<- mean(theta2, na.rm = TRUE)
BC<- 2*Estimate_Standard$Original -Boot1
DBC<- (3*Estimate_Standard$Original-3*Boot1+Boot2)
Estimate_DoubleBootstrap<-list(Original = Estimate_Standard$Original, Bootstrap=BC, Double_Bootstrap=DBC, oValues=theta1, iValues=theta2)
}
if(JC==TRUE){
N=length(d1)
Test=NULL
for(v in 1:N){
d2<-d1[-v]
try(Test[v]<-estimate(d2)$Original)
}
Estimate_Jackknife<-list(Original = Estimate_Standard$Original, Jackknife=(N*Estimate_Standard$Original-(N-1)*mean(Test)))
}
if(B>0){return(Estimate_Bootstrap)}
if(JC==TRUE){return(Estimate_Jackknife)}
if(DB[1]!=0){return(Estimate_DoubleBootstrap)}
if(B==0 && JC==FALSE && DB[1]==0){return(Estimate_Standard)}
}
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