Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

DOI10.1214/13-AIHP545zbMath1302.60052arXiv1204.2355OpenAlexW2963789414MaRDI QIDQ405492

S. Valère Bitseki Penda, Hacène Djellout

Publication date: 5 September 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2355

zbMATH Keywords

martingaleleast-squares estimatorbifurcating autoregressive processbinary tree structuresuperexponential convergence

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Martingales with discrete parameter (60G42) Nonparametric estimation (62G05) Large deviations (60F10)

Related Items (8)

Moderate deviation principle in nonlinear bifurcating autoregressive models ⋮ A phase transition for large values of bifurcating autoregressive models ⋮ Autoregressive functions estimation in nonlinear bifurcating autoregressive models ⋮ Moderate deviations for estimators under exponentially stochastic differentiability conditions ⋮ A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes ⋮ The asymptotic behaviors for least square estimation of multi-casting autoregressive processes ⋮ Deviation inequalities for bifurcating Markov chains on Galton−Watson tree ⋮ Central limit theorem for bifurcating Markov chains under pointwise ergodic conditions

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