Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains models
Abstract
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator. Unlike the work of Bitseki and Gorgui (2021), it is interesting to see that the distinction of the two regimes disappears and that we are able to get moderate deviation principle for large values of the ergodic rate. It is also interesting and surprising to see that for moderate deviation principle, the ergodic rate begins to have an impact on the choice of the bandwidth for values smaller than in the context of central limit theorem studied by Bitseki and Delmas (2021).
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.00808
 Bibcode:
 2021arXiv210900808V
 Keywords:

 Mathematics  Probability;
 Mathematics  Statistics Theory;
 62G05;
 62F12;
 60F10;
 60J80
 EPrint:
 27