pbuniv: Parametric Bootstrap (Univariate)
In jeksterslabds/jeksterslabRboot: Jekster's Lab Linear Bootstrap Utilities

Description Usage Arguments Details Value Author(s) References See Also Examples

Generates B number of parametric bootstrap samples from estimated parameters of original univariate sample data. data is referred to as the empirical distribution

\hat{ F }_{ \mathcal{ Distribution } }

. The default distribution is

\mathcal{ N } ≤ft( \hat{ μ }, \hat{ σ }^2 \right) %(\#eq:boot-pb-norm)

. The univariate distribution and parameters used in the data generating process can be specified using rFUN and ....

pbuniv(
  n,
  rFUN = rnorm,
  ...,
  B = 2000L,
  par = FALSE,
  ncores = NULL,
  mc = TRUE,
  lb = FALSE,
  cl_eval = FALSE,
  cl_export = FALSE,
  cl_expr,
  cl_vars,
  rbind = NULL
)

`n`	Integer. Sample size.
`rFUN`	Function. Data generating function to generate univariate data.
`...`	Arguments to pass to `rFUN`.
`B`	Integer. Number of bootstrap samples.
`par`	Logical. If `TRUE`, use multiple cores. If `FALSE`, use `lapply()`.
`ncores`	Integer. Number of cores to use if `par = TRUE`. If unspecified, defaults to `detectCores() - 1`.
`mc`	Logical. If `TRUE`, use `parallel::mclapply()`. If `FALSE`, use `parallel::parLapply()` or `parallel::parLapplyLB()`. Ignored if `par = FALSE`.
`lb`	Logical. If `TRUE` use `parallel::parLapplyLB()`. If `FALSE`, use `parallel::parLapply()`. Ignored if `par = FALSE` and `mc = TRUE`.
`cl_eval`	Logical. Execute `parallel::clusterEvalQ()` using `cl_expr`. Ignored if `mc = TRUE`.
`cl_export`	Logical. Execute `parallel::clusterExport()` using `cl_vars`. Ignored if `mc = TRUE`.
`cl_expr`	Expression. Expression passed to `parallel::clusterEvalQ()` Ignored if `mc = TRUE`.
`cl_vars`	Character vector. Names of objects to pass to `parallel::clusterExport()` Ignored if `mc = TRUE`.
`rbind`	NULL or logical. If `rbind = NULL`, returns the list produced. If `TRUE`, uses `rbind()` to bind the rows of the list produced. If `FALSE`, uses `cbind()` to bind the columns of the list produced. Test that each element of the output list has the appropriate dimensions for binding before using this option.

For more details and examples see the following vignettes:

Notes: Intro to NB

Notes: Intro to PB

Returns a list of length B of parametric bootstrap samples.

Ivan Jacob Agaloos Pesigan

Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York, N.Y: Chapman & Hall.

Wikipedia: Bootstrapping (statistics)

Other bootstrap functions: nb(), pbmvn()

n <- 5
B <- 5
# normal distribution---------------------------------------------------------
mu <- 100
sigma2 <- 225
sigma <- sqrt(sigma2)
x <- rnorm(
  n = n,
  mean = mu,
  sd = sigma
)
muhatthetahat <- mean(x)
Sigmahatthetahat <- sd(x)
xstar <- pbuniv(
  n = n,
  rFUN = rnorm,
  B = B,
  mean = muhatthetahat,
  sd = Sigmahatthetahat
)
str(xstar)
# binomial distribution-------------------------------------------------------
n_trials <- 1
p <- 0.50
x <- rbinom(
  n = n,
  size = n_trials,
  prob = p
)
phat <- mean(x) / n_trials
xstar <- pbuniv(
  n = n,
  rFUN = rbinom,
  B = B,
  size = n_trials,
  prob = phat
)
str(xstar)