pbmvn: Parametric Bootstrap (Multivariate Normal) from \boldsymbol{...
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 using estimated parameters from the original sample data. data is referred to as the empirical distribution with the following distributional assumption

\hat{ F }_{ \mathcal{ N }_{k} ≤ft( \boldsymbol{ \hat{ μ } } ≤ft( \boldsymbol{ \hat{ θ } } \right) , \boldsymbol{ \hat{ Σ } } ≤ft( \boldsymbol{ \hat{ θ } } \right) \right) } . %(\#eq:boot-pb-mvn)

Bootstrap samples are generated from a multivariate normal distribution using the fitted model-implied mean vector and variance-covariance matrix.

pbmvn(
  n,
  muhatthetahat,
  Sigmahatthetahat,
  tol = 1e-06,
  empirical = FALSE,
  B = 2000L,
  par = FALSE,
  ncores = NULL,
  mc = TRUE,
  lb = FALSE,
  cl_eval = FALSE,
  cl_export = FALSE,
  cl_expr,
  cl_vars
)

`n`	Integer. Sample size.
`muhatthetahat`	Vector. Mean vector as a function of estimated parameters or the fitted model-implied mean vector \boldsymbol{ \hat{ μ } } ≤ft( \boldsymbol{ \hat{ θ } } \right) %(\#eq:boot-pb-mvn-mu) .
`Sigmahatthetahat`	Matrix. Variance-covariance matrix as a function of estimated parameters or the fitted model-implied variance-covariance matrix \boldsymbol{ \hat{ Σ } } ≤ft( \boldsymbol{ \hat{ θ } } \right) %(\#eq:boot-pb-mvn-Sigma) .
`tol`	Numeric. Tolerance (relative to largest variance) for numerical lack of positive-definiteness in `Sigma`.
`empirical`	Logical. If `TRUE`, `mu` and `Sigma` specify the empirical not population mean and covariance matrix.
`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`.

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(), pbuniv()

B <- 5L
Sigmahatthetahat <- matrix(
  data = c(
    82.37344,
    70.55922,
    17.83930,
    70.55922,
    112.57145,
    -75.98558,
    17.83930,
    -75.98558,
    338.46263
  ),
  nrow = 3
)
muhatthetahat <- c(
  108.3060,
  105.3324,
  103.4009
)
Xstar <- pbmvn(
  n = 5,
  Sigmahatthetahat = Sigmahatthetahat,
  muhatthetahat = muhatthetahat,
  B = B
)
str(Xstar)