jackVarRegen {boodd} | R Documentation |
Jackknife Variance Estimator for Regenerative Processes
Description
Estimates the variance of a statistic applied to a vector or a matrix using a jackknife procedure tailored for regenerative processes, in particular recurrent Markov chains.
Usage
jackVarRegen(x, func, ..., atom, small = NULL, s = median(x))
Arguments
x |
A vector or a matrix representing the data. |
func |
The function applied to each sample. |
... |
Optional additional arguments for the |
atom |
A numeric value or a string; an atom of the Markov chain in the atomic case. |
small |
An optional object of class |
s |
A real number specifying the center of the small set. Default is the median of |
Details
The jackVarRegen
function is a versatile tool for estimating the jackknife variance
in cases of statistics based on regenerative blocks.
It accommodates variable length blocks and is
effective for both finite state and general Markov chains.
It calls jackVarRegen.atom
and jackVarRegen.smallEnsemble
, respectively in
the atomic and the general case.
Value
Returns a scalar or a covariance matrix, depending on whether the function func
is univariate or multivariate. For a function returning a vector of length
p, the output will be a covariance matrix of size p x p.
References
Bertail, P. and Clémençon. S. (2006). Regeneration-based statistics for Harris recurrent Markov chains, 1-54. Lecture notes in Statistics 187. Springer.
Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.
Quenouille, M.H. (1949). Approximate tests of correlation in time-series. J. Roy. Statist. Soc., Ser. B, 11, 68-84.
Quenouille, M. H. (1956). Notes on bias in estimation , Biometrika, 43, 353–360.
See Also
jackVar
,
jackFunc
,
regenboot
,
jackFuncRegen
,
jackFuncBlock
,
jackVarRegen.atom
,
jackVarRegen.smallEnsemble
.
Examples
acgt <- c("A", "C", "G", "T")
probs <- c(.3, .1, .3, .3)
n <- 100
atom <- "A"
set.seed(1)
y <- sample(acgt, n, prob=probs, repl=TRUE)
propAtom <- function(x) {
tbl <- as.vector(table(x))
prop <- tbl[1] / length(x)
return(prop)
}
jackVarRegen(y, propAtom, atom=atom)