# boot.stationary: Generate Index for Stationary Bootstrapping In maotai: Tools for Matrix Algebra, Optimization and Inference

## 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

 `1` ```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

\insertRef

politis_stationary_1994maotai

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```## 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) ```

maotai documentation built on Feb. 3, 2022, 5:09 p.m.