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 |
... |
Optional additional arguments for the |
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)