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)


[Package boodd version 0.1 Index]