Integral, Measure and Martingale

2017年7月12日星期三

Adaptive procedures for non-parameter tests

x<-c(51.9,56.9,45.2,52.3,59.5,41.4,46.4,45.1,53.9,42.9,41.5,55.2,32.9,54.0,45.0)
y<-c(59.2,49.1,54.4,47.0,55.9,34.9,62.2,41.6,59.3,32.7,72.1,43.8,56.8,76.7,60.3)

drive4=function(x,y){
n1=length(x)
n2=length(y)
n=n1+n2
cb=(1:n)/(n+1)

const=(n1*n2)/(n*(n-1))#p550

p1=phi1(cb)
var1=const*sum(p1^2)

p2=phi2(cb)
var2=const*sum(p2^2)

p3=phi3(cb)
var3=const*sum(p3^2)

p4=phi3(cb)
var4=const*sum(p4^2)

vars=c(var1,var2,var3,var4)
allxy=c(x,y)

rall=rank(allxy)/(n+1)
ind=c(rep(0,n1),rep(1,n2))

s1=sum(ind*phi1(rall))
s2=sum(ind*phi2(rall))
s3=sum(ind*phi3(rall))
s4=sum(ind*phi4(rall))

tests=c(s1,s2,s3,s4)
ztests=tests/sqrt(vars)

list(vars=vars,tests=tests,ztests=ztests)
}

phi1=function(u){
phi1=2*u-1
phi1
}

phi2=function(u){
phi2=sign(2*u-1)
phi2
}

phi3=function(u){
n=length(u)
phi3=rep(0,n)
for(i in 1:n){
if(u[i]<=0.25){phi3[i]=4*u[i]-1}
if(u[i]>0.75){phi3[i]=4*u[i]-3}
}
phi3
}

phi4=function(u){
n=length(u)
phi4=rep(0.5,n)
for(i in 1:n){
if(u[i]<=0.5){phi4[i]=4*u[i]-3/2}
}
phi4
}
drive4(x,y)

v<-c(x,y)
sv<-sort(v)
q<-quantile(sv, c(0.05, 0.25,0.5,0.75,0.95))

U005<-c()
M05<-c()
L005<-c()
U05<-c()
L05<-c()

for(i in 1:30){
if (sv[i]<q[1]){L005[i]=sv[i]}
if (sv[i]>q[2]&sv[i]<q[4]){M05[i]=sv[i]}
if (sv[i]>q[4]){U005[i]=sv[i]}
if (sv[i]>q[3]){U05[i]=sv[i]}
if (sv[i]<q[3]){L05[i]=sv[i]}
}

L005
M05
U005
U05
L05

Um005<-mean(U005,na.rm=TRUE)
Um005

Mm05<-mean(M05,na.rm=TRUE)
Mm05

Um05<-mean(U05,na.rm=TRUE)
Um05

Lm05<-mean(L05,na.rm=TRUE)
Lm05

Lm005<-mean(L005,na.rm=TRUE)
Lm005

Q1<-(Um005-Mm05)/(Mm05-Lm005)
Q1

Q2=(Um005-Lm005)/(Um05-Lm05)
Q2