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

Autor: Adélaïde Olivier, S. Valère Bitseki Penda
Přispěvatelé: Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire de Mathématiques d'Orsay (LMO), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Statistics and Probability
Type (model theory)
01 natural sciences
Moderate deviation principle
Bifurcating autoregressive process
Bifurcating Markov chain
010104 statistics & probability
Bernoulli's principle
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Applied mathematics
[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]
0101 mathematics
Mathematics
Markov chain
010102 general mathematics
Nonparametric statistics
Estimator
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
Binary tree
[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]
MSC: 62G05
62G20
60J80
60F05
60F10
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Nonlinear system
Autoregressive model
Moderate deviations
Statistics
Probability and Uncertainty
Nonparametric estimation
[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Nadaraya–Watson estimator
Zdroj: Statistics and Probability Letters
Statistics and Probability Letters, Elsevier, 2018, 138, pp.20-26. 〈10.1016/j.spl.2018.02.037〉
Statistics and Probability Letters, Elsevier, 2018, 138, pp.20-26. ⟨10.1016/j.spl.2018.02.037⟩
ISSN: 0167-7152
DOI: 10.1016/j.spl.2018.02.037〉
Popis: International audience; 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.
Databáze: OpenAIRE
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