jackVarRegen.atom {boodd}R Documentation

Jackknife Variance Estimator for Atomic Markov Chains

Description

Provides a regenerative jackknife estimator of the variance of a function applied to atomic Markov chains.

Usage

jackVarRegen.atom(x, func, atom, ...)

Arguments

x

A vector or a matrix representing the Markov chain.

func

The function to apply to each sample.

atom

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

...

Optional additional arguments for the func function.

Details

This function uses a regenerative approach to estimate the jackknife variance of a statistic for atomic Markov chains. It segments the chain at the specified atom into independent blocks. The function func, having output size equal to p, is applied to the data with each regenerative block removed in turn to finally compute an empirical variance of the obtained values. This approach is particularly useful for atomic Markov chains.

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 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.

Examples

 B=1000
 set.seed(5)
 bb=0*(1:B)
 cc=0*(1:B)
 for (i in 1:B) {
   ts=genMM1(100,2,4)
   vv=function(ts){as.numeric(var(ts))}
   bb[i]=mean(ts)
   cc[i]=jackVarRegen.atom(ts,mean,atom=0)}
 var(bb)  # true variance of the mean (evaluated by Monte-Carlo)
 mean(cc) # mean of the variance estimators over the Monte-Carlo simulations

[Package boodd version 0.1 Index]