Deviation inequalities for bifurcating Markov chains on Galton-Watson tree
Abstract
We provide deviation inequalities for properly normalized sums of bifurcating Markov chains on Galton-Watson tree. These processes are extension of bifurcating Markov chains (which was introduced by Guyon to detect cellular aging from cell lineage) in case the index set is a binary Galton-Watson process. As application, we derive deviation inequalities for the least-squares estimator of autoregressive parameters of bifurcating autoregressive processes with missing data. These processes allow, in case of cell division, to take into account the cell's death. The results are obtained under an uniform geometric ergodicity assumption of an embedded Markov chain.
Keywords
Cite
@article{arxiv.1302.3768,
title = {Deviation inequalities for bifurcating Markov chains on Galton-Watson tree},
author = {Siméon Valère Bitseki Penda},
journal= {arXiv preprint arXiv:1302.3768},
year = {2014}
}
Comments
24 pages, 2 figures. arXiv admin note: text overlap with arXiv:1111.7303 by other authors