Deviation inequalities for bifurcating Markov chains on Galton-Watson tree

2013/02/15 by Siméon Valère Bitseki Penda, Penda, Siméon Valère Bitseki
Mathematics · #2000. Primary 60E15 #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:2000. #msc:60E15 #msc:60J10 #msc:60J80 #secondary 60J10

paper · pdf · doi:10.48550/arxiv.1302.3768

24 pages, 2 figures. arXiv admin note: text overlap with arXiv:1111.7303 by other authors

arxiv created 2013/02/15 · arxiv updated 2014/01/17

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.

Citations

• Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application

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