boot.stationary {maotai}

Generate Index for Stationary Bootstrapping

Description

Assuming data being dependent with cardinality N, boot.stationary returns a vector of index that is used for stationary bootstrapping. To describe, starting points are drawn from uniform distribution over 1:N and the size of each block is determined from geometric distribution with parameter p.

Usage

boot.stationary(N, p = 0.25)

Arguments

N

the number of observations.

p

parameter for geometric distribution with the size of each block.

Value

a vector of length N for moving block bootstrap sampling.

References

Politis DN, Romano JP (1994). “The Stationary Bootstrap.” Journal of the American Statistical Association, 89(428), 1303. ISSN 01621459.

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 stationary bootstrapping
nreps   = 50
vec.mu  = rep(0,nreps)
vec.var = rep(0,nreps)
for (i in 1:nreps){
   sample.id = boot.stationary(100)
   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)