pairwise.se {Monte.Carlo.se}

Standard Errors for Paired Comparisons of Monte Carlo Output Summaries

Description

pairwise.se — gives jackknife and bootstrap SEs for all the pairwise difference or ratios of Monte Carlo summaries.

Usage

pairwise.se(
  x,
  xcol,
  diff = TRUE,
  digits = 4,
  B = 0,
  seed = NULL,
  summary.f,
  ...
)

Arguments

x

vector from N independent Monte Carlo replications

xcol

columns of x to be used

diff

If TRUE (default), uses differences; if diff=F, uses ratios

digits

number of digits to retain in output data frame

B

B=0 means use jackknife (default), B>0 means use bootstrap with B resamples, If B>0, then a seed must be given to start the bootstrap resampling

seed

seed=NULL (default) used with jackknife, otherwise needs a positive integer

summary.f

summary function computed from x (e.g., mean, median, var)

...

Additional arguments to be passed

Details

Suppose that an N-vector of Monte Carlo output (thus, a sample of size N) is produced from N independent Monte Carlo samples, and a summary statistic like the mean or variance is to be reported in a table. pairwise.se gives Monte Carlo standard errors (SEs) for all pairwise differences or ratios of these summary statistics. The vignette vignette("Example3", package = "Monte.Carlo.se") is a detailed account of using pairwise.se.

Value

Returns a data frame of the indiviual ith and jth column summaries (summi and summj), the differences or ratios of those summaries (summary), MC standard error of the difference or ratio, MC sample size N, method (jackknife or bootstrap), B and seed if bootstrap is used

Author(s)

Dennis Boos, Kevin Matthew, Jason Osborne

References

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.

Examples

# Using the output data matrix hold generated in vignette Example3, 
# calculate jackknife and bootstrap standard errors
# for the differences and ratios of the CV estimates.

# Jackknife SE of Differences of CVs

# pairwise.se(hold,xcol=10:12,summary.f=cv)
# elem  summi  summj summary     se  t.stat    N    method
# 1 10 11 0.6884 0.7030 -0.0146 0.0299 -0.4877 1000 Jackknife
# 2 10 12 0.6884 0.6489  0.0395 0.0195  2.0274 1000 Jackknife
# 3 11 12 0.7030 0.6489  0.0541 0.0311  1.7374 1000 Jackknife

# Jackknife SE of Ratios of CVs

# pairwise.se(hold,xcol=10:12,diff=FALSE,summary.f=cv)
# elem  summi  summj summary     se  t.stat    N    method
# 1 10 11 0.6884 0.7030  0.9792 0.0429 -0.4833 1000 Jackknife
# 2 10 12 0.6884 0.6489  1.0608 0.0321  1.8972 1000 Jackknife
# 3 11 12 0.7030 0.6489  1.0833 0.0475  1.7531 1000 Jackknife

# Bootstrap SE of Differences of CVs

# pairwise.se(hold,xcol=10:12,B=1000,seed=770,summary.f=cv)
# elem  summi  summj summary     se  t.stat    B seed    N    method
# 1 10 11 0.6884 0.7030 -0.0146 0.0278 -0.5250 1000  770 1000 Bootstrap
# 2 10 12 0.6884 0.6489  0.0395 0.0182  2.1671 1000  770 1000 Bootstrap
# 3 11 12 0.7030 0.6489  0.0541 0.0303  1.7844 1000  770 1000 Bootstrap

# Bootstrap SE of Ratios of CVs

# pairwise.se(hold,xcol=10:12,diff=FALSE,B=1000,seed=770,summary.f=cv)
# elem  summi  summj summary     se  t.stat    B seed    N    method
# 1 10 11 0.6884 0.7030  0.9792 0.0390 -0.5316 1000  770 1000 Bootstrap
# 2 10 12 0.6884 0.6489  1.0608 0.0292  2.0797 1000  770 1000 Bootstrap
# 3 11 12 0.7030 0.6489  1.0833 0.0430  1.9372 1000  770 1000 Bootstrap