• Corpus ID: 237385920

Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains models

@inproceedings{Penda2021ModerateDP,
  title={Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains models},
  author={Sim'eon Valere Bitseki Penda},
  year={2021}
}
  • S. Penda
  • Published 2 September 2021
  • Mathematics
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator. Unlike the work of Bitseki and Gorgui (2021), it is interesting to see that the distinction of the two regimes disappears and that we are able to get moderate deviation principle for large values of the ergodic rate. It is also interesting and surprising to see… 

References

SHOWING 1-10 OF 25 REFERENCES
Central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models
TLDR
It is proved the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations of Markov chains, motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait.
Adaptive estimation for bifurcating Markov chains
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,
Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model
TLDR
An adaptive estimator for the stationary distribution of a bifurcating Markov Chain on the basis of dimension jump methods and an algorithm to select the best constant in the penalty is proposed.
Moderate deviation principles for bifurcating Markov chains: case of functions dependent of one variable
. The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are
Deviation inequalities, moderate deviations and some limit theorems for bifurcating Markov chains with application
Firstly, under geometric ergodicity assumption, we provide some limit theo- rems and some probability inequalities for bifurcating Markov chains introduced by Guyon to detect cellular aging from cell
Moderate deviation principle in nonlinear bifurcating autoregressive models
Moderate Deviations and Large Deviations for Kernel Density Estimators
AbstractLet fn be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in ℝd. It is proved
Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next
Autoregressive functions estimation in nonlinear bifurcating autoregressive models
TLDR
An asymptotic test for the equality of the two autoregressive functions is developed which is implemented both on simulated and real data and proves almost sure convergence, asymPTotic normality giving the bias expression when choosing the optimal bandwidth.
Confidence bands for densities, logarithmic point of view
Let f be a probability density and C be an interval on which f is bounded away from zero. By establishing the limiting distribution of the uniform error of the kernel estimates fn of f, Bickel and
...
...