Project

Eco-Dep

Goal: Modelling population dynamics is of paramount importance in many fields of applications. In ecology, it is a matter to understand the dynamics and life history of various species across different environments. Indeed, environmental changes can generate rapid changes on the composition of a given population, its length, its phenotypic trait or also its genotype distribution. In demography, we are generally interested in predicting human life-span as well as the population structure with critical implication in pension systems and public policy decision making. However, these dynamics raise a number of problems to which historical experience offers no answers. This research proposal considers in some integrated way the modelling of populations growth and biodiversity prediction using cutting edge stochastic models with a specific focus on ecological problems. First, we will consider applications of Taylor's law. We will comprehensively introduce a new variant related to self-normalisation issue based on weak dependence conditions. This will consider some of the stylised facts encountered when working with real-world datasets. Besides, we will investigate challenges facing marine ecology, especially those related to changing environment and its impact on the marine species. We will introduce new modelling frameworks for populations dynamics incorporating, for instance, covariates and we will investigate their statistical properties. These problems involve isotonic models parsimony in the presence of non-linearity and non-stationarity. Causality relationships will be determined. Finally, applications will be devoted, among others, to the effects of climate change on coral reefs, the modelling abundances in ecology and the prediction of marine ecosystem, see http://doukhan.u-cergy.fr/EcoDep.html
Activities are on http://doukhan.u-cergy.fr/activities.html
Several pages may be of interest
A- Members http://doukhan.u-cergy.fr/members.html
B-Seminary http://doukhan.u-cergy.fr/seminary.html
C-Lectures http://doukhan.u-cergy.fr/education.html
D-Publications http://doukhan.u-cergy.fr/publications.html

Date: 1 July 2020 - 30 June 2024

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Paul Doukhan
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Paul Doukhan
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This paper provides extensions of the work on subsampling by Bertail et al. (2004) for strongly mixing case to weakly dependent case by application of the results of Doukhan and Louhichi (1999). We investigate properties of smooth and rough subsampling estimators for distributions of converging and extreme statistics when the underlying time series is η or λ-weakly dependent.
We propose a novel estimator of the autocorrelation function in presence of missing observations. We establish the consistency, the asymptotic normality, and we derive deviation bounds for various classes of weakly dependent stationary time series, including causal or non causal models. In addition, we introduce a modified version periodogram defined from these autocorrelation estimators and derive asymptotic distribution of linear functionals of this estimator. Comment: 16 pages
The aim of this paper is to provide a comprehensive introduction for the study of ℓ1-penalized estimators in the context of dependent observations. We define a general ℓ1-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO [Tib96] in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study this estimator under various dependence assumptions.
Paul Doukhan
added an update
Paul Doukhan
added a project goal
Modelling population dynamics is of paramount importance in many fields of applications. In ecology, it is a matter to understand the dynamics and life history of various species across different environments. Indeed, environmental changes can generate rapid changes on the composition of a given population, its length, its phenotypic trait or also its genotype distribution. In demography, we are generally interested in predicting human life-span as well as the population structure with critical implication in pension systems and public policy decision making. However, these dynamics raise a number of problems to which historical experience offers no answers. This research proposal considers in some integrated way the modelling of populations growth and biodiversity prediction using cutting edge stochastic models with a specific focus on ecological problems. First, we will consider applications of Taylor's law. We will comprehensively introduce a new variant related to self-normalisation issue based on weak dependence conditions. This will consider some of the stylised facts encountered when working with real-world datasets. Besides, we will investigate challenges facing marine ecology, especially those related to changing environment and its impact on the marine species. We will introduce new modelling frameworks for populations dynamics incorporating, for instance, covariates and we will investigate their statistical properties. These problems involve isotonic models parsimony in the presence of non-linearity and non-stationarity. Causality relationships will be determined. Finally, applications will be devoted, among others, to the effects of climate change on coral reefs, the modelling abundances in ecology and the prediction of marine ecosystem, see http://doukhan.u-cergy.fr/EcoDep.html
Several pages may be of interest