fastNadaraya {boodd} | R Documentation |
Nadaraya-Watson Estimator for Transition Densities for Markov chains.
Description
Calculates the Nadaraya-Watson estimator for estimating the transition densities of a Markov chain. This function is particularly useful for approximating transition kernels in Markov chain analysis.
Usage
fastNadaraya(x, bandwidth)
Arguments
x |
A numeric vector representing a Markov process. |
bandwidth |
A real number; the kernel bandwidth smoothing parameter |
Details
The fastNadaraya
function computes the estimated transition densities
p_n(X_i, X_{i+1})
of a Markov chain. It is based on the Nadaraya kernel-type
estimator for the transition density, with a bandwidth bandwidth
provided by the user.
This function is used in conjunction with findBestEpsilon
to determine optimal small set for the Regenerative Block Bootstrap regenboot
.
Value
Returns a numeric vector of size length(x) - 1
, containing
the estimated transition densities for each state transition in the Markov chain.
References
Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.
Bertail, P., Clémençon, S. (2006a). Regenerative Block Bootstrap for Markov Chains. Bernoulli, 12, 689-712.
Bertail, P. and Clémençon, S. (2006). Regeneration-based statistics for Harris recurrent Markov chains, pages 1-54. Number 187 in Lecture notes in Statistics. Springer.
Radulović, D. (2006). Renewal type bootstrap for Markov chains. Test, 13, 147-192.
See Also
findBestEpsilon
,
regenboot
,
bandw1
.
Examples
x = arima.sim(1000, model=list(ar=c(0.4)))
h = bandw1(x)
fastNadaraya(x,h)