Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains

S. Valère Bitseki Penda

Stochastic Processes and their Applications, 2023, vol. 158, issue C, 282-314

Abstract: Bitseki and Delmas (2022) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains. We complete their work by proving a moderate deviation principle for this estimator. Unlike the work of Bitseki and Gorgui (2022), 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 (2022).

Keywords: Bifurcating Markov chains; Bifurcating auto-regressive process; Binary trees; Density estimation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.01.004

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