Moderate deviation principle in nonlinear bifurcating autoregressive models

Abstract : Recently, nonparametric techniques have been proposed to study bifurcating autoregressive processes. One can build Nadaraya–Watson type estimators of the two autoregressive functions as in Bitseki Penda et al. (Bitseki Penda S.V., Escobar-Bach M., Guillin A.,Transportation cost-information and concentration inequalities for bifurcating Markov chains, Bernoulli, 23 (2017), pp. 3213-3242 ; Bitseki Penda S.V., Hoffmann M., Olivier A., Adaptive estimation for bifurcating Markov chains, Bernoulli, 23 (2017), pp. 3598-3637) and Bitseki Penda and Olivier (Bitseki Penda S.V., Olivier A., Autoregressive functions estimation in nonlinear bifurcating autoregressive models, Stat. Inference Stoch. Process., 20 (2017), pp. 179-210). In the present work, we prove moderate deviation principe for these estimators.
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Siméon Valère Bitseki Penda, Adélaïde Olivier. Moderate deviation principle in nonlinear bifurcating autoregressive models. Statistics and Probability Letters, Elsevier, 2018, 138, pp.20-26. ⟨10.1016/j.spl.2018.02.037⟩. ⟨hal-01710079⟩

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