boot.mblock {maotai}

Generate Index for Moving Block Bootstrapping

Description

Assuming data being dependent with cardinality N, boot.mblock returns a vector of index that is used for moving block bootstrapping.

Usage

boot.mblock(N, b = max(2, round(N/10)))

Arguments

N

the number of observations.

b

the size of a block to be drawn.

Value

a vector of length N for moving block bootstrap sampling.

References

Kunsch HR (1989). “The Jackknife and the Bootstrap for General Stationary Observations.” The Annals of Statistics, 17(3), 1217–1241.

Examples

## example : bootstrap confidence interval of mean and variances
vec.x = seq(from=0,to=10,length.out=100)
vec.y = sin(1.21*vec.x) + 2*cos(3.14*vec.x) + rnorm(100,sd=1.5)
data.mu  = mean(vec.y)
data.var = var(vec.y)

## apply moving block bootstrapping
nreps   = 50
vec.mu  = rep(0,nreps)
vec.var = rep(0,nreps)
for (i in 1:nreps){
   sample.id = boot.mblock(100, b=10)
   sample.y  = vec.y[sample.id]
   vec.mu[i]  = mean(sample.y)
   vec.var[i] = var(sample.y)
   print(paste("iteration ",i,"/",nreps," complete.", sep=""))
}

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
plot(vec.x, vec.y, type="l", main="1d signal")  # 1d signal
hist(vec.mu, main="mean CI", xlab="mu")         # mean
abline(v=data.mu, col="red", lwd=4)
hist(vec.var, main="variance CI", xlab="sigma") # variance
abline(v=data.var, col="blue", lwd=4)
par(opar)