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 func function.

atom

A numeric value or a string; an atom of the Markov chain in the atomic case.

small

An optional object of class smallEnsemble. It can be created optimally using findBestEpsilon.

s

A real number specifying the center of the small set. Default is the median of x.

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)

[Package boodd version 0.1 Index]