Laurence Marsalle

Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson process, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

Statistical study of asymmetry in cell lineage data

A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the dependence structure within genealogical trees. Its main new feature is the joint use of all available information from several data sets instead of single data set estimation, to avoid the drawbacks of low accuracy for estimators or low power for tests on small single trees. The data is modeled by an asymmetric bifurcating autoregressive process and possibly missing observations are taken into account by modeling the genealogies with a two-type Galton-Watson process. Least-squares estimators of the unknown parameters of the processes are given and symmetry tests are derived. Results are applied on real data of Escherichia coli division and an empirical study of the convergence rates of the estimators and power of the tests is conducted on simulated data.

Performance of an optimal receiver in the presence of alpha-stable and Gaussian noises

This paper deals with the optimal (in the maximum likelihood sense) detection performance of binary transmission in a mixture of a Gaussian noise and an impulsive interference modeled as an alpha-stable process. The main contribution is in the Monte Carlo simulation that shows that the Gaussianity assumption for the test statistic as reported in earlier works is not valid unless a very large number of repetitions is used.

Hausdorff Measures and Capacities for Increase Times of Stable Processes

AbstractLet X be a real-valued stable process. It is known that X possesses increase times iff ℙ(X1 > 0) >

Detection of cellular aging in a Galton-Watson process

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Asymmetry tests for bifurcating auto-regressive processes with missing data

([1]). In that case, we specify the exact Hausdorff function of the set of increase times, and characterize the subsets of [0,+∞) which contain increase times in terms of their capacity.

SLOW POINTS AND FAST POINTS OF LOCAL TIMES

Holder regularity which plays a key role in fractal geometry raises an increasing interest in probability and statistics. In this paper we discuss various aspects of local and global regularity for stochastic processes and random fields. As a main result we show the invariability of the pointwise Holder exponent of a continuous and nowhere differentiable random field which has stationary increments and satisfies a zero-one law. We also survey some recent uses of Holder spaces in limit theorems for stochastic processes and statistics.