Nothing
TS_kernel <-
function(data,band,quantile)
{
sigma=0;Xg=0;
n=dim(data)[2];
hwidth=band/n;
x=c(1:n)/n
Snw <- matrix(0, nrow = n, ncol = n)
## Calculate the hat matrix for the Nadaraya-Watson kernel estimator
In <- diag(rep(1, n)) ## identity matrix
for(j in 1:n){
y <- In[,j]
Snw[,j] <- ksmooth(x, y, kernel = "normal", bandwidth = hwidth, x.points = x)$y
}
#ad_df=2*sum(diag(Snw))-sum(diag(Snw%*%t(Snw)));
ad_df=sum(diag(Snw))
for (k in 1:dim(data)[1])
{
x=c(1:n)/n
diff41=data[k,];
# kernel smoothing
hwidth=band/n;
d41=ksmooth(x,diff41,"normal",bandwidth=hwidth)
#sigma1_ut=mad(y1$y-L1) #0
sigma <- sqrt(sum((d41$y-diff41)^2) / (length(diff41)-ad_df))
Xg[k]=sigma;
}
Xg[which(Xg==0)]=min(Xg[which(Xg>0)]);
#
hist(Xg^2,xlab=expression(paste(hat(sigma)^2)), main="")
#abline(v=quantile(Xg, quantile),col=2)
CHQBC_1_adjB=Xg;
if (quantile > 0)
{
CHQBC_1_adjB=Xg+quantile(Xg, quantile)
}
Ts_yvec=0;
Sign=0;
# Start Kernel Smoothing #
for (k in 1:dim(data)[1])
{
x=c(1:n)/n
# normalized variance
diff=data[k,]/CHQBC_1_adjB[k];
hwidth=band/n;
#y1=ksmooth(x,L1,"normal",bandwidth=hwidth)
#y4=ksmooth(x,L4,"normal",bandwidth=hwidth)
d41=ksmooth(x,diff,"normal",bandwidth=hwidth)
diffy4y1=d41$y
#### Build the test statistics #####
# minimax test
#library(kernlab)
#rbfdot(sigma=1)
ytest.vec=diffy4y1
Ts_yvec[k]=mean(ytest.vec^2)
Sign[k]=sign(sum(ytest.vec))
}
Tsb = 1/(2*(band*0.37)*sqrt(pi));
vu=sqrt(2*pi)/(2*pi*n*(band*0.37))
#delta=1/(sqrt(2)*n)
#d=1/(sqrt(2*pi)*band*0.37/n)
Amax=Snw%*%Snw;
eigenvalue=as.numeric(eigen(Amax)$values)
d= sum(eigenvalue)^2/sum(eigenvalue^2)
delta= sum(eigenvalue)/(n*d)
Test.adj=Ts_yvec
TS_kn=(((Test.adj/(delta*d))^(1/3)-(1-2/(9*d)))/sqrt(2/(9*d)))
return(list("TS"=TS_kn,"TS_sign"=Sign, "Tmean"=Ts_yvec))
}
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