Hugo Harari-Kermadec

Empirical φ ∗ -Divergence Minimizers for Hadamard Differentiable Functionals

We study some extensions of the empirical likelihood method, when the Kullback distance is replaced by some general convex divergence or φ-discrepancy. We show that this generalized empirical likelihood method is asymptotically valid for general Hadamard differentiable functionals.

Regenerative block empirical likelihood for Markov chains

Empirical likelihood (EL) is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical EL method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalisation of EL based on the construction of blocks of increasing random length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalisation for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results.

A nonparametric method for penetrance function estimation.

In diseases caused by a deleterious gene mutation, knowledge of age‐specific cumulative risks is necessary for medical management of mutation carriers. When pedigrees are ascertained through at least one affected individual, ascertainment bias can be corrected by using a parametric method such as the Probands phenotype Exclusion Likelihood, or PEL, that uses a survival analysis approach based on the Weibull model. This paper proposes a nonparametric method for penetrance function estimation that corrects for ascertainment on at least one affected: the Index Discarding EuclideAn Likelihood or IDEAL. IDEAL is compared with PEL, using family samples simulated from a Weibull distribution and under alternative models. We show that, under Weibull assumption and asymptotic conditions, IDEAL and PEL both provide unbiased risk estimates. However, when the true risk function deviates from a Weibull distribution, we show that the PEL might provide biased estimates while IDEAL remains unbiased. Genet. Epidemiol. 2008.

On the use of Empirical Likelihood for non-Gaussian clutter covariance matrix estimation

This paper presents an improved estimation scheme when the clutter distribution is unknown. The Empirical Likelihood (EL) is a recent semi-parametric estimation method which allows to estimate unknown parameters by using information contained in the observed data such as constraints on the parameter of interest as well as an a priori structure. The aim of this paper is twofold. First, the empirical likelihood is briefly introduced and then, some constraints on the unknown parameters are added. To illustrate this situation, we focus on the problem of estimating the clutter covariance matrix when this matrix is assumed to be Toeplitz. Finally, theoretical results are emphasized by several simulations corresponding to real situations: the mixture of a Gaussian (thermal noise) and a non-Gaussian (clutter) noise.

Tuition fees and social segregation: lessons from a natural experiment at the University of Paris 9-Dauphine

ABSTRACT Using a natural experiment, a sharp rise in tuition fees in some of the programmes at the University of Paris 9-Dauphine, we study the impact of tuition fees on students’ pathways, and outcomes. We apply an optimal matching method to the national database of students’ registrations (SISE) to define a typology of pathways. We then use a nonordered multinomial logit model to evaluate the impact of the rise in tuition fees on the types of pathways selected by the university. We show that there is a significant impact on these pathways. The increase in tuition fees reduces geographic and social mobility, thereby accentuating the phenomena of social segregation. Furthermore, contrary to what some of the studies assert, the rise does not appear to encourage greater effort: we find no impact on the graduation success rate.

Financing Higher Education: A Contributory Scheme

In this paper, we study the higher education financing based on the classical contributory versus self-funded pension funding scheme. We provide a brief discussion of how a system based on student debt can be seen ’funded’ and why it fails to ensure equity and efficiency and funding for the longer term. We also define a contributory financing scheme for higher education based on income tax and social security contributions, and study its strengths and weaknesses. By contributory, we mean a scheme that ensures free access to university, providing for students’ expenses and the costs of research and teaching. We show that such a system would be efficient and equitable, and we discuss under what conditions it would be efficient. We show also that it would prevent polarization in the higher education system. We conclude with an implementation of our contributory financing scheme in the case of France (it increases university funding by €5bn and provides €19bn for students’ expenditure) and illustrate the effect of such a scheme on some typical households.