arXiv subjects

Anne Gegout-Petit

Publications and source records attributed to Anne Gegout-Petit.

3 recordsLinked to original sources

arXiv2015

Likelihood inference for incompletely observed stochastic processes: ignorability conditions

We develop a study of ignorability and conditions thereof for likelihood inference in the framework of stochastic processes. We define a coarsening model for processes which includes discrete-time observations as well as censored continuous-time observations and applies to continuous state-space processes as well as counting processes. For preparing the work we recall formulas for manipulating marginal and conditional likelihood ratios (which can apply to stochastic processes). Ignorability is defined in terms of local equality of two likelihood ratios. We give static conditions of ignorability and then dynamical conditions which are more interpretable. We illustrate the use of the dynamical conditions of ignorability in problems of censoring, missing data and joint modelling.

math.ST↗

arXiv2009

Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

math.PR↗

arXiv2007

A general dynamical statistical model with possible causal interpretation

We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic processes, as in Aalen (1987); then we define direct and indirect influence. We propose a definition of causal influence using the concepts of ``physical system''. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of this paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for HIV load and CD4 counts. We show its inadequacy to capture causal influences while on the contrary known mechanisms of HIV infection can be expressed directly through a system of differential equations.

math.ST↗