6533b827fe1ef96bd128580b

RESEARCH PRODUCT

MODERATE DEVIATION PRINCIPLES FOR KERNEL ESTIMATOR OF INVARIANT DENSITY IN BIFURCATING MARKOV CHAINS MODELS

Siméon Valère Bitseki Penda

subject

[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]60J80[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Bifurcating Markov chains[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]binary trees[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]bifurcating auto-regressive process62F12density estimation Mathematics Subject Classification (2020): 62G0560F10

description

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).

yearjournalcountryeditionlanguage
2021-09-02
https://hal.science/hal-03331911