#Bootstrapping example
library(boot)

?galaxies
hist(galaxies)
set.seed(102)
gal.boot<-boot(galaxies,function(x,i) median(x[i]),R=1000)
gal.boot
summary(gal.boot)
plot(gal.boot)
str(gal.boot)
summary(gal.boot$t)
sd(gal.boot$t)

xbci<-boot.ci(gal.boot,conf=c(0.9,0.95),type=c("norm","basic","perc","bca"))
xbci

qt<-quantile(gal.boot$t,probs=c(0.025,0.05,0.5,0.95,0.975))
qt

str(xbci)
xbci$n
(xbci$n[1,3]+xbci$n[1,2])/2


?shoes
data(shoes)
names(shoes)
attach(shoes)

plot(A,B)
hist(B-A)
ipcp(data.frame(A,B))
iplot(A,B-A)

mean(B-A)
var(B-A)
t.test(B-A)
shoes.boot<-boot(B-A,function(x,i) mean(x[i]),R=1000)

mean.fun<-function(d,i){
 n<-length(i)
 c(mean(d[i]),(n-1)*var(d[i])/n^2)
 }

shoes.boot2<-boot(B-A,mean.fun,R=1000)
boot.ci(shoes.boot2,type=c("perc","stud","basic"))
shoes.boot2

9*var(B-A)/100

plot(shoes.boot2)
JavaGD()
plot(shoes.boot)


#Bootstrapping Modelle
library(simpleboot)
?airquality
attach(airquality)
set.seed(30)

lmodel <- lm(Ozone ~ Wind)

#Resampling von FŠllen
lboot <- lm.boot(lmodel, R = 1000)
summary(lboot)
plot(lboot)

#Resampling von Residuen
lboot2 <- lm.boot(lmodel, R = 1000, rows = FALSE)
summary(lboot2)

#Verteilungen von den Stichprobenstatistiken
rsquareB <- samples(lboot,  "rsquare")
hist(rsquareB)

s <- samples(lboot,  "coef")
hist(s)
hist(s[1,])
hist(s[2,])
plot(s[1,],s[2,])

rssB <- samples(lboot, "rss")
hist(rssB)

#Bootstrapping loess
l1<-loess(Ozone~Wind)
lboot3<- loess.boot(l1, R = 1000)

JavaGD()
plot(lboot3)

JavaGD()
plot(lboot3,all.lines=TRUE)