
Adaptive estimation for bifurcating Markov chains
Hoffmann, Marc; Olivier, Adélaïde; Valère Bitseki Penda, Siméon (2017), Adaptive estimation for bifurcating Markov chains, Bernoulli, 23, 4B, p. 3598 - 3637. 10.3150/16-BEJ859
View/ Open
Type
Article accepté pour publication ou publiéDate
2017Journal name
BernoulliVolume
23Number
4BPublisher
International Statistical Institute
Pages
3598 - 3637
Publication identifier
Metadata
Show full item recordAbstract (EN)
In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric wavelet thresholding estimation procedures: in a second part, we construct nonparametric estimators of the transition density of a BMC, of its mean transition density and of the corresponding invariant density, and show smoothness adaptation over various multivariate Besov classes under $L^p$ -loss error, for $1\leq p<\infty$. We prove that our estimators are (nearly) optimal in a minimax sense. As an application, we obtain new results for the estimation of the splitting size-dependent rate of growth-fragmentation models and we extend the statistical study of bifurcating autoregressive processes.Subjects / Keywords
Binary trees; Bifurcating Markov chains; Nonparametric adaptive estimation; Bifurcating autoregressive process; Growth-fragmentation processes; Minimax rates of convergence; Deviations inequalitiesRelated items
Showing items related by title and author.
-
Bitseki Penda, Siméon Valère; Roche, Angelina (2020) Article accepté pour publication ou publié
-
Valère Bitseki Penda, Siméon; Olivier, Adélaïde (2017) Article accepté pour publication ou publié
-
Hoffmann, Marc; Olivier, Adélaïde (2016) Article accepté pour publication ou publié
-
Johannes, Schmidt-Hieber; Munk, Axel; Hoffmann, Marc (2012) Article accepté pour publication ou publié
-
Féron, Olivier; Gruet, Pierre; Hoffmann, Marc (2020) Article accepté pour publication ou publié