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 |
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