Moderate deviation principle in nonlinear bifurcating autoregressive models

Principe de déviations modérées pour des modèles bifurquants autorégressifs non-linéaires

Siméon Valère Bitseki Penda (1) , Adélaïde Olivier (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 LMO - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Moderate deviation principle; Nadaraya–Watson estimator; Binary tree; Bifurcating autoregressive process; Nonparametric estimation; Bifurcating Markov chain

Domaines: Théorie [stat.TH]; Probabilités [math.PR]; Statistiques [math.ST]

Siméon Valère Bitseki Penda, Adélaïde Olivier. Moderate deviation principle in nonlinear bifurcating autoregressive models. Statistics and Probability Letters, 2018, 138, pp.20-26. ⟨10.1016/j.spl.2018.02.037⟩. ⟨hal-01710079⟩