Monte.Carlo.se (version 0.1.1)

boot.se: Bootstrap Standard Error

Description

boot.se -- gives a bootstrap standard error (SE=estimated standard deviation)

Usage

boot.se(x, B, theta, ...)

Value

Returns the bootstrap SE of theta(x)

Arguments

x

vector of data

B

number of bootstrap resamples (replications)

theta

function (statistic) applied to the data (e.g., mean, median, var)

...

Additional arguments to be passed

Author

Dennis Boos, Kevin Matthew, Jason Osborne

Details

The code was modified from code associated with the appendix of Efron and Tibshirani (1993)

References

Efron and Tibshirani (1993), _An Introduction to the Bootstrap_.

Boos, D. D., and Osborne, J. A. (2015), "Assessing Variability of Complex Descriptive Statistics in Monte Carlo Studies using Resampling Methods," International Statistical Review, 25, 775-792.

See Also

jack.se -- mc.se.vector -- mc.se.matrix

Examples

# \donttest{
# simple example, data from Boos and Osborne (2105, Table 3)
# using theta=coefficient of variation mean/sd

x=c(1,2,79,5,17,11,2,15,85)
cv=function(x){sd(x)/mean(x)}

cv(x)
# [1] 1.383577

# bootstrap SE using B=1000

set.seed(384)
boot.se(x,B=1000,theta=cv)
# [1] 0.3416897

# More complex example using two samples, se for ratio of means
# data from Higgins (2003, problem 4.4, p. 142), LDH readings on 7 patients

before=c(89,90,87,98,120,85,97)
after=c(76,101,84,86,105,84,93)

# requires function using row index as "data", real data is extra parameter xdata
ratio.means <- function(index,xdata)
 {mean(xdata[index,1])/mean(xdata[index,2])}

ratio.means(index=1:7,xdata=data.frame(before,after))
# [1] 1.058824

# boostrap SE for ratio of means

set.seed(2917)
boot.se(x=1:7,B=1000,theta=ratio.means,xdata=data.frame(before,after))
# [1] 0.03576659

# To illustrate use with Monte Carlo output, first create some sample data
# 10,000 samples of size 15 from the Laplace (double exp) distribution

N<-10000
set.seed(450)
z1 <- matrix(rexp(N*15),nrow=N)
z2 <- matrix(rexp(N*15),nrow=N)
z<-(z1-z2)/sqrt(2)              # subtract standard exponentials
out.m.15   <- apply(z,1,mean)
out.t20.15 <- apply(z,1,mean,trim=0.20)
out.med.15 <- apply(z,1,median)


# The three datasets (out.m.15,out.t20.15,out.med.15) each contain 10000 values.
# If we want use the variance of each column in a table, then to get
# the Monte Carlo standard error of those 3 variances,

set.seed(250)
boot.se(out.m.15,B=1000,theta = var)
# [1] 0.0009373835

boot.se(out.t20.15,B=1000,theta = var)
# [1] 0.0007086057

boot.se(out.med.15,B=1000,theta = var)
# [1] 0.0008307258
# } # ends donttest
# Function Code

boot.se<-function(x, B, theta, ...){
  call <- match.call()
  n <- length(x)
  bootsam <- matrix(sample(x, size = n * B, replace = T), nrow = B)
  thetastar <- apply(bootsam, 1, theta, ...)
  se <- sd(thetastar)
  return(se)
  }