jackVarRegen.smallEnsemble {boodd}R Documentation

Jackknife Variance Estimation for General Harris Markov Chains

Description

Estimates the jackknife variance of a function applied to general Harris Markov chains using a regenerative approach and a smallEnsemble object.

Usage

jackVarRegen.smallEnsemble(x, func, small, ...)

Arguments

x

A vector or matrix representing the data from a general Harris Markov chain.

func

The function to apply to each sample.

small

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

...

Optional additional arguments for the func function.

Details

The function uses a regenerative approach to estimate the 

jackknife variance for functions applied to general Harris Markov chains. It relies on a smallEnsemble object to define the regenerative structure of the data. It segments the chain using an estimated Nummelin splitting trick to create almost independent blocks. The function func, having output size equal to p, is applied to the data with each approximate regenerative block removed in turn to finally compute an empirical variance of the obtained values.

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.

See Also

jackVar, jackFunc, regenboot, jackFuncRegen, jackFuncBlock, jackVarRegen.

Examples


B=10
bb=0*(1:B)
cc=0*(1:B)
dd=0*(1:B)
for (i in 1:B) {
  ts=arima.sim(list(ar=0.4),200)
   vv=function(ts){as.numeric(var(ts))}
   bb[i]=mean(ts)
   cc[i]=jackVarRegen.smallEnsemble(ts,mean, small= findBestEpsilon(ts))}
var(bb)  
mean(cc) 
# Monte Carlo simulations
mean(dd) 


[Package boodd version 0.1 Index]