Package 'resample'

Title: Resampling Functions
Description: Bootstrap, permutation tests, and jackknife, featuring easy-to-use syntax.
Authors: Tim Hesterberg
Maintainer: Tim Hesterberg <[email protected]>
License: BSD_3_clause + file LICENSE
Version: 0.6
Built: 2025-02-14 03:40:11 UTC
Source: https://github.com/cran/resample

Help Index

Overview of the resample package

Description

Resampling functions, including one- and two-sample bootstrap and permutation tests, with an easy-to-use syntax.

Details

See library(help = resample) for version number, date, etc.

Data Sets

A list of datasets is at resample-data,

Main resampling functions

The main resampling functions are: bootstrap, bootstrap2, permutationTest,
permutationTest2.

Methods

Methods for generic functions include: print.resample, plot.resample,
hist.resample, qqnorm.resample, and quantile.resample.

Confidence Intervals

Functions that calculate confidence intervals for bootstrap and bootstrap2 objects:
CI.bca, CI.bootstrapT, CI.percentile, CI.t.

Samplers

Functions that generate indices for random samples: samp.bootstrap, samp.permute.

Low-level Resampling Function

This is called by the main resampling functions, but can also be called directly: resample.

New Versions

I will post the newest versions to https://www.timhesterberg.net/r-packages. See that page to join a list for announcements of new versions.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

Examples

data(Verizon)
ILEC <- with(Verizon, Time[Group == "ILEC"])
CLEC <- with(Verizon, Time[Group == "CLEC"])

#### Sections in this set of examples
### Different ways to specify the data and statistic
### Example with plots and confidence intervals.


### Different ways to specify the data and statistic
# This code is flexible; there are different ways to call it,
# depending on how the data are stored and on the statistic.


## One-sample Bootstrap

# Ordinary vector, give statistic as a function
bootstrap(CLEC, mean)

# Vector by name, give statistic as an expression
bootstrap(CLEC, mean(CLEC))

# Vector created by an expression, use the name 'data'
bootstrap(with(Verizon, Time[Group == "CLEC"]), mean(data))

# A column in a data frame; use the name of the column
temp <- data.frame(foo = CLEC)
bootstrap(temp, mean(foo))

# Put function arguments into an expression
bootstrap(CLEC, mean(CLEC, trim = .25))

# Put function arguments into a separate list
bootstrap(CLEC, mean, args.stat = list(trim = .25))


## One-sample jackknife

# Syntax is like bootstrap, e.g.
jackknife(CLEC, mean)


## One-sample permutation test

# To test H0: two variables are independent, exactly
# one of them just be permuted. For the CLEC data,
# we'll create an artificial variable.
CLEC2 <- data.frame(Time = CLEC, index = 1:length(CLEC))

permutationTest(CLEC2, cor(Time, index),
                resampleColumns = "index")
# Could permute "Time" instead.

# resampleColumns not needed for variables outside 'data'
permutationTest(CLEC, cor(CLEC, 1:length(CLEC)))



### Two-sample problems
## Different ways to specify data and statistic

## Two-sample bootstrap

# Two data objects (one for each group)
bootstrap2(CLEC, data2 = ILEC, mean)

# data frame containing y variable(s) and a treatment variable
bootstrap2(Verizon, mean(Time), treatment = Group)

# treatment variable as a separate object
temp <- Verizon$Group
bootstrap2(Verizon$Time, mean, treatment = temp)


## Two-sample permutation test

# Like bootstrap2, e.g.
permutationTest2(CLEC, data2 = ILEC, mean)


### Example with plots and confidence intervals.

boot <- bootstrap2(CLEC, data2 = ILEC, mean)
perm <- permutationTest2(CLEC, data2 = ILEC, mean,
                         alternative = "greater")
par(mfrow = c(2,2))
hist(boot)
qqnorm(boot)
qqline(boot$replicates)
hist(perm)


# P-value
perm
# Standard error, and bias estimate
boot

# Confidence intervals
CI.percentile(boot) # Percentile interval
CI.t(boot)  # t interval using bootstrap SE
# CI.bootstrapT and CI.bca do't currently support two-sample problems.

# Statistic can be multivariate.
# For the bootstrap2, it must have the estimate first, and a standard
# error second (don't need to divide by sqrt(n), that cancels out).
bootC <- bootstrap(CLEC, mean, seed = 0)
bootC2 <- bootstrap(CLEC, c(mean = mean(CLEC), sd = sd(CLEC)), seed = 0)
identical(bootC$replicates[, 1], bootC2$replicates[, 1])

CI.percentile(bootC)
CI.t(bootC)
CI.bca(bootC)
CI.bootstrapT(bootC2)
# The bootstrapT is the most accurate for skewed data, especially
# for small samples.

# By default the percentile and BCa intervals are "expanded", for
# better coverage in small samples. To turn this off:
CI.percentile(bootC, expand = FALSE)

One and two sample bootstrap sampling and permutation tests.

Description

Basic resampling. Supply the data and statistic to resample.

Usage

bootstrap(data, statistic, R = 10000,
          args.stat = NULL, seed = NULL, sampler = samp.bootstrap,
          label = NULL, statisticNames = NULL, block.size = 100,
          trace = FALSE)
bootstrap2(data, statistic, treatment, data2 = NULL, R = 10000,
          ratio = FALSE,
          args.stat = NULL, seed = NULL, sampler = samp.bootstrap,
          label = NULL, statisticNames = NULL, block.size = 100,
          trace = FALSE)
permutationTest(data, statistic, R = 9999,
          alternative = "two.sided", resampleColumns = NULL,
          args.stat = NULL, seed = NULL, sampler = samp.permute,
          label = NULL, statisticNames = NULL, block.size = 100,
          trace = FALSE, tolerance = .Machine$double.eps ^ 0.5)
permutationTest2(data, statistic, treatment, data2 = NULL, R = 9999,
          alternative = "two.sided", ratio = FALSE, paired = FALSE,
          args.stat = NULL, seed = NULL, sampler = samp.permute,
          label = NULL, statisticNames = NULL, block.size = 100,
          trace = FALSE, tolerance = .Machine$double.eps ^ 0.5)

Arguments

data

vector, matrix, or data frame.

statistic

a function, or expression (e.g. mean(myData, trim = .2).

R

number of replicates (bootstrap samples or permutation resamples).

treatment

a vector with two unique values. For two-sample applications, suppy either treatment or data2.

data2

an object like data; the second sample.

alternative

one of "two.sided", "greater", or "less". If statistic returns a vector, this may be a vector of the same length.

ratio

logical, if FALSE then statistics for two samples are combined using statistic1 - statistic2 (the statistics from the two samples). If TRUE, it uses statistic1 / statistic2.

resampleColumns

integer, or character (a subset of the column names of data); if supplied then only these columns of the data are permuted. For example, for a permutation test of the correlation of x and y, only one of the variables should be permuted.

args.stat

a list of additional arguments to pass to statistic, if it is a function.

paired

logical, if TRUE then observations in data and data2 are paired, and permutations are done within each pair. Not yet implemented.

seed

old value of .Random.seed, or argument to set.seed.

sampler

a function for resampling, see help(samp.bootstrap).

label

used for labeling plots (in a future version).

statisticNames

a character vector the same length as the vector returned by statistic.

block.size

integer. The R replicates are done this many at a time.

trace

logical, if TRUE an indication of progress is printed.

tolerance

when computing P-values, differences smaller than tolerance (absolute or relative) between the observed value and the replicates are considered equal.

Details

There is considerable flexibility in how you specify the data and statistic.

For the statistic, you may supply a function, or an expression. For example, if data = x, you may specify any of

  • statistic = mean

  • statistic = mean(x)

  • statistic = mean(data)

If data is a data frame, the expression may refer to columns in the data frame, e.g.

  • statistic = mean(x)

  • statistic = mean(myData$x)

  • statistic = mean(myData[, "x"])

If data is not just the name of an object, e.g. data = subset(myData, age > 17), or if data2 is supplied, then use the name 'data', e.g.

  • statistic = colMeans(data)

Value

a list with class "bootstrap", "bootstrap2", "permutationTest",
or "permutationTest2", that inherits from "resample", with components:

observed

the value of the statistic for the original data.
replicates

a matrix with R rows and p columns.
n

number of observations in the original data, or vector of length 2 in two-sample problems.
p

length(observed).
R

number of replications.
seed

the value of the seed at the start of sampling.
call

the matched call.
statistics

a data frame with p rows, with columns "observed", "mean" (the mean of the replicates), and other columns appropriate to resampling; e.g. the bootstrap objects have columns "SE" and "Bias", while the permutation test objects have "Alternative" and "PValue".

The two-sample versions have an additional component:

resultsBoth

containing resampling results from each data set. containing two components, the results from resampling each of the two samples. These are bootstrap objects; in the permutationTest2 case they are the result of sampling without replacement.

There are functions for printing and plotting these objects, in particular print, hist, qqnorm, plot (currently the same as hist), quantile.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

resample-package, samp.bootstrap, CI.percentile, CI.t.

Examples

# See full set of examples in resample-package, including different
# ways to call the functions depending on the structure of the data.
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
bootC <- bootstrap(CLEC, mean)
bootC
hist(bootC)
qqnorm(bootC)

Front end to cat

Description

Call cat, with sep="" and/or newline at end.

Usage

cat0(...)
cat0n(...)
catn(...)

Arguments

...

R objects, like for cat

Details

cat0 and cat0n call cat with sep = "". catn and cat0n print a final newline).

Value

None (invisible NULL).

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

cat, paste0.

Examples

cat("Print this")
# That printed without a final newline.
catn("Print this")
cat0n("10,", "000")

Bootstrap confidence intervals

Description

Bootstrap confidence intervals - percentile method or t interval.

Usage

CI.percentile(x, confidence = 0.95, expand = TRUE, ...,
              probs = sort(1 + c(-1, 1) * confidence) / 2)
CI.t(x, confidence = 0.95, expand = TRUE,
              probs = sort(1 + c(-1, 1) * confidence) / 2)
CI.bca(x, confidence = 0.95,
              expand = TRUE, L = NULL,
              probs = sort(1 + c(-1, 1) * confidence) / 2)
CI.bootstrapT(x, confidence = 0.95,
              probs = sort(1 + c(-1, 1) * confidence) / 2)

Arguments

x

a bootstrap or bootstrap object.

confidence

confidence level, between 0 and 1. The default 0.95 gives a 95% two-sided interval.

expand

logical, if TRUE then use modified percentiles for better small-sample accuracy.

...

additional arguments to pass to quantile.resample and quantile.

probs

probability values, between 0 and 1. confidence = 0.95 corresponds to probs = c(0.025, 0.975). If this is supplied then confidence is ignored.

L

vector of length n, empirical influence function values. If not supplied this is computed using jackknife.

Details

CI.bootstrapT assumes the first dimension of the statistic is an estimate, and the second is proportional to a SE for the estimate. E.g. for bootstrapping the mean, they could be the mean and s. This is subject to change.

CI.bca and CI.bootstrapT currently only support a single sample.

Value

a matrix with one column for each value in probs and one row for each statistic.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

References

This discusses the expanded percentile interval: Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, https://arxiv.org/abs/1411.5279.

See Also

bootstrap, bootstrap2, ExpandProbs (for the expanded intervals).

Examples

# See full set of examples in resample-package, including different
# ways to call all four functions depending on the structure of the data.
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
bootC <- bootstrap(CLEC, mean, seed = 0)
bootC2 <- bootstrap(CLEC, c(mean = mean(CLEC), sd = sd(CLEC)), seed = 0)
CI.percentile(bootC)
CI.t(bootC)
CI.bca(bootC)
CI.bootstrapT(bootC2)

Column variances and standard deviations for matrices.

Description

Quick and dirty function for column variances and standard deviations.

Usage

colVars(x, na.rm = FALSE)
colStdevs(x, ...)

Arguments

x

data frame, matrix, or vector. These versions do not support higher-dimensional arrays.

na.rm

logical. Should missing values (including NaN) be omitted from the calculations?

...

other arguments passed to colVars.

Value

A numeric or complex array of suitable size, or a vector if the result is one-dimensional. The dimnames (or names for a vector result) are taken from the original array.

Note

There are better versions of these functions in the aggregate package
https://www.timhesterberg.net/r-packages.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

colSums, var, sd.

Examples

x <- matrix(rnorm(12), 4)
colVars(x)
colStdevs(x)

Deprecated functions.

Description

Deprecated functions

Arguments

...

arguments to pass to the replacement functions.

Details

limits.percentile, limits.t and limits.bootstrapT have been renamed "CI.*".

Value

See the replacement functions.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

CI.percentile, CI.t, CI.bootstrapT.

Calculate modified probabilities for more accurate confidence intervals

Description

Compute modified quantiles levels, for more accurate confidence intervals. Using these levels gives sider intervals, with closer to desired coverage.

Usage

ExpandProbs(probs, n)

Arguments

probs

vector of numerical values between 0 and 1.

n

number of observations.

Details

Bootstrap percentile confidence interval for a sample mean correspond roughly to

xˉ±zασ^\bar x \pm z_\alpha \hat\sigma

instead of

xˉ±tα,n−1s\bar x \pm t_{\alpha,n-1} s

where

σ^=(n−1)/ns\hat\sigma = \sqrt{(n-1)/n s}

is like s but computed using a divisor of n instead of n-1. Similarly for other statistics, the bootstrap percentile interval is too narrow, typically by roughly the same proportion.

This function finds modified probability levels probs2, such that

zprobs2(n−1)/n=tprobs,n−1z_{\mbox{probs2}} \sqrt{(n-1)/n} = t_{\mbox{probs}, n-1}

z_probs2 sqrt((n-1)/n) = t_probs,n-1 so that for symmetric data, the bootstrap percentile interval approximately matches the usual $t$ confidence interval.

Value

A vector like probs, but with values closer to 0 and 1.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

References

This discusses the expanded percentile interval: Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, https://arxiv.org/abs/1411.5279.

See Also

CI.percentile, CI.bca,

Examples

probs <- c(0.025, 0.975)
n <- c(5, 10, 20, 40, 100, 200, 1000)
outer(probs, n, ExpandProbs)

Conditional Data Selection

Description

This is equivalent to {if(test) yes else no}. The advantages of using this function are better formatting, and a more natural syntax when the result is being assigned; see examples below.

With 5 arguments, this is equivalent to {if(test1) yes else if(test2) u else v} (where arguments are given by name, not position).

Usage

IfElse(test, yes, no, ...)

Arguments

test

logical value; if TRUE return yes.
yes

any object; this is returned if test is TRUE.
no

normally any object; this is returned if test is FALSE. If there are more than three arguments this should be logical.
...

there should be 3, 5, 7, etc. arguments to this function; arguments 1, 3, 5, etc. should be logical values; the other arguments (even numbered, and last) are objects that may be returned.

Details

test should be a scalar logical, and only one of yes or no is evaluated, depending on whether test = TRUE or test = FALSE, and yes and no may be any objects. In contrast, for ifelse, test is normally a vector, both yes and no are evaluated, even if not used, and yes and no are vectors the same length as test.

Value

with three arguments, one of yes or no. With k arguments, one of arguments 2, 4, ..., k-1, k.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

ifelse, if.

Examples

IfElse(TRUE, "cat", "dog")
IfElse(FALSE, "one", TRUE, "two", "three")
IfElse(FALSE, "one", FALSE, "two", "three")

One sample jackknife

Description

Basic resampling. Supply the data and statistic to resample.

Usage

jackknife(data, statistic, args.stat = NULL,
          label = NULL, statisticNames = NULL, trace = FALSE)

Arguments

data

vector, matrix, or data frame.

statistic

a function, or expression (e.g. mean(myData, trim = .2).

args.stat

a list of additional arguments to pass to statistic, if it is a function.

label

used for labeling plots (in a future version).

statisticNames

a character vector the same length as the vector returned by statistic.

trace

logical, if TRUE an indication of progress is printed.

Value

a list with class "jackknife" that inherits from "resample", with components:

observed

the value of the statistic for the original data.
replicates

a matrix with R rows and p columns.
n

number of observations in the original data, or vector of length 2 in two-sample problems.
p

length(observed).
R

number of replications.
seed

the value of the seed at the start of sampling.
call

the matched call.
statistics

a data frame with p rows, with columns "observed", "mean" (the mean of the replicates), and other columns appropriate to resampling; e.g. the bootstrap objects have columns "SE" and "Bias", while the permutation test objects have "Alternative" and "PValue".

There are functions for printing and plotting these objects, in particular print, plot, hist, qqnorm, quantile.

Note

The current version only handles a single sample.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

resample-package.

Examples

# See full set of examples in resample-package
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
jackknife(CLEC, mean)

Methods for common generic functions for resample objects

Description

Methods for common generic functions. The methods operate primarily on the replicates (resampled statistics).

Usage

## S3 method for class 'resample'
print(x, ...)
## S3 method for class 'resample'
hist(x, ..., resampleColumns = 1:x$p, xlim = NULL,
                xlab = NULL, main = "", col = "blue", border = 0,
                breaks = "FD", showObserved = TRUE,
                legend = TRUE, args.legend = NULL)
## S3 method for class 'resample'
plot(x, ...)
## S3 method for class 'resample'
qqnorm(y, ..., resampleColumns = 1:y$p, ylab = NULL,
                pch = if(y$R < 100) 1 else ".")
## S3 method for class 'resample'
quantile(x, ...)

Arguments

x, y

a "resample" object, usually produced by one of bootstrap, bootstrap2, permutationTest, or permutationTest2.

...

additional arguments passed to the corresponding generic function.
For plot.resample, these are passed to hist.resample.

resampleColumns

integer subscripts, or names of statistics. When a statistic is a vector, resampleColumns may be used to select which resampling distributions to plot.

xlim

limits for the x axis.

xlab, ylab

x and y axis labels.

main

main title

col

color used to fill bars, see hist.

border

color of the order around the bars, see hist.

breaks

method for computing breaks, see hist.

showObserved

logical, if TRUE then vertical lines are shown at the observed statistic and mean of the bootstrap replicates.

legend

logical, if TRUE a legend is added. Not used if showObserved = FALSE.

args.legend

NULL or a list of arguments to pass to legend.

pch

plotting character, see par.

Details

hist.resample displays a histogram overlaid with a density plot, with the observed value of the statistic indicated.

plot.resample currently just calls hist.resample.

Value

For quantile.resample, a matrix with one row for each statistic and one column for each value in probs. This uses type=6 when calling quantile, for wider (more accurate) quantiles than the usual default.

The other functions are not called for their return values.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

resample-package, bootstrap, bootstrap2, jackknife, permutationTest,
permutationTest2, quantile.

Examples

# See full set of examples in resample-package
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
bootC <- bootstrap(CLEC, mean, seed = 0)
print(bootC)
hist(bootC)
qqnorm(bootC)
quantile(bootC, probs = c(.25, .975))
# That is the percentile interval with expand = FALSE
CI.percentile(bootC)

Compute quantiles using type = 6

Description

Front end to quantile, using type = 6 (appropriate for resampling)

Usage

Quantile(x, ..., type = 6)

Arguments

x

resample object, numerical object, or other object with a method for quantile.

...

Other arguments passed to quantile.

type

With type=6 and 99 observations, the k% quantile is the k'th smallest observation; this corresponds to equal probability above the largest observation, below the smallest observation, and between each pair of adjacent observations.

Details

This is a front end to quantile.

Value

A vector or matrix of quantiles.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

quantile

Examples

quantile(1:9, .2)
Quantile(1:9, .2)

Nonparametric resampling

Description

This function is called by bootstrap and other resampling functions to actually perform resampling, but may also be called directly.

Usage

resample(data, resampleFun, sampler, R = 10000, seed = NULL,
         statisticNames = NULL, block.size = 100,
         trace = FALSE, ..., observedIndices = 1:n,
         call = match.call())

Arguments

data

vector, matrix, or data frame.

resampleFun

a function with argument data and ii, that calculates a statistic of interest for data[ii] or data[ii, , drop=FALSE], for a vector or matrix, respectively.

sampler

a function like samp.bootstrap or samp.permute.

R

number of resamples.

seed

old value of .Random.seed, or argument to set.seed.

statisticNames

a character vector the same length as the vector returned by statistic.

block.size

integer. The R replicates are done this many at a time.

trace

logical, if TRUE an indication of progress is printed.

...

addition arguments passed to sampler.

observedIndices

integer vector of indices, used for calculating the observed value. When this is called by bootstrap2 or permutationTest2, those should be indices corresponding to one sample in a merged data set.

call

typically the call to bootstrap or another function that calls resample. This may be a character string, e.g. when called from bootstrap2.

Details

This is called by bootstrap, bootstrap2, permutationTest, and permutationTest2 to actually perform resampling. The results are passed back to the calling function, which may add additional components and a class, which inherits from "resample".

This may also be called directly. In contrast to the other functions, where you have flexibility in how you specify the statistic, here resampleFun must be a function.

Value

an object of class "resample"; this is a list with components:

observed

the observed statistic, length p.
replicates

a matrix with R rows and p columns.
n

number of observations
p

the length of the statistic returned by resampleFun.
R

number of resamples.
seed

the value of seed when this function is called.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

See Also

bootstrap, bootstrap2, permutationTest, permutationTest2, samp.bootstrap, samp.permute.

For an overview of all functions in the package, see resample-package.

Examples

# See full set of examples in resample-package, including different
# ways to call all the functions depending on the structure of the data.
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
bootC <- bootstrap(CLEC, mean, seed = 0)
bootC

Data sets for resampling examples

Description

Data sets for use in examples.

Details

TV has measurements of minutes of commercials per half-hour, for "Basic" and "Extended" (extra-cost) cable TV stations.

Verizon has repair times, with two groups, CLEC and ILEC, customers of the "Competitive" and "Incumbent" local exchange carrior.

DATA SETS

TV 10 observations: Time,Cable Verizon 1687 observations: Time,Group

Source

The TV and Verizon datasets are used in What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum

References

Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, https://arxiv.org/abs/1411.5279.

See Also

See resample-package for an overview of resampling functions.

Examples

data(TV); summary(TV)
Basic <- with(TV, Time[Cable == "Basic"])
Extended <- with(TV, Time[Cable == "Extended"])

data(Verizon); summary(Verizon)
ILEC <- with(Verizon, Time[Group == "ILEC"])
CLEC <- with(Verizon, Time[Group == "CLEC"])

Generate indices for resampling

Description

Generate indices for resampling.

Usage

samp.bootstrap(n, R, size = n - reduceSize, reduceSize = 0)
samp.permute(n, R, size = n - reduceSize, reduceSize = 0,
             groupSizes = NULL, returnGroup = NULL)

Arguments

n

sample size. For two-sample permutation tests, this is the sum of the two sample sizes.

R

number of vectors of indices to produce.

size

size of samples to produce. For example, to do "what-if" analyses, to estimate the variability of a statistic had the data been a different size, you may specify the size.

reduceSize

integer; if specified, then size = n - reduceSize (for each sample or stratum). This is an alternate way to specify size. Typically bootstrap standard errors are too small; they correspond to using n in the divisor of the sample variance, rather than n-1. By specifying reduceSize = 1, you can correct for that bias. This is particularly convenient in two-sample problems where the sample sizes differ.

groupSizes

NULL, or vector of positive integers that add to n.

returnGroup

NULL, or integer from 1 to length(groupSizes). groupSizes and returnGroup must be supplied together; then full permutations are created, but only subsets of size groupSizes[returnGroup] is returned.

Details

To obtain disjoint samples without replacement, call this function multiple times, after setting the same random number seed, with the same groupSizes but different values of returnGroup. This is used for two-sample permutation tests.

If groupSizes is supplied then size is ignored.

Value

matrix with size rows and R columns (or groupSizes(returnGroup) rows). Each column contains indices for one bootstrap sample, or one permutation.

Note

The value passed as R to this function is typically the block.size argument to bootstrap and other resampling functions.

Author(s)

Tim Hesterberg [email protected],
https://www.timhesterberg.net/bootstrap-and-resampling

References

This discusses reduced sample size: Hesterberg, Tim C. (2004), Unbiasing the Bootstrap-Bootknife Sampling vs. Smoothing, Proceedings of the Section on Statistics and the Environment, American Statistical Association, 2924-2930, https://drive.google.com/file/d/1eUo2nDIrd8J_yuh_uoZBaZ-2XCl_5pT7.

See Also

resample-package.

Examples

samp.bootstrap(7, 8)
samp.bootstrap(7, 8, size = 6)
samp.bootstrap(7, 8, reduceSize = 1)

# Full permutations
set.seed(0)
samp.permute(7, 8)

# Disjoint samples without replacement = subsets of permutations
set.seed(0)
samp.permute(7, 8, groupSizes = c(2, 5), returnGroup = 1)
set.seed(0)
samp.permute(7, 8, groupSizes = c(2, 5), returnGroup = 2)