Modèle autogressif à valeurs entières avec arrondi

National audienceDans cet exposé, nous présentons une nouvelle classe de modèles autorégressifs à valeurs entières basés sur l'opérateur d'arrondi

Le Processus Autorégressif d'Arrondi d'Ordre p ( RINAR(p) )

International audienceles séries chronologiques à valeur entières sont fréquentes dans la pratique. Avant la fin des années 80 de telle observations étaient traitées par des modèles réels classiques. Plus tard, des classes de modèle possédant les mêmes propriétés que les modèles réels et respectant la nature entière des observations ont éte introduites. Ces classes ont plusieurs limites. Nous proposons un nouveau modèle pour générer des observations entières. Ce modèle est basé sur l'opérateur arrondi. Notons que l'arrondi est une idée naturelle pour récolter des données entières à partir des observations réelles. Ensuite, nous étudions les propriétés de ce modèle

An enquiry into potential graduate entrepreneurship:is higher education turning off the pipeline of graduate entrepreneurs?

Purpose: In today’s global economy, high in talent but low in growth, the capability and skills mismatch between the output of universities and the demands of business has escalated to a worrying extent for graduates. Increasingly, university students are considering alternatives to a lifetime of employment, including their own start-up, and becoming an entrepreneur. The literature indicates a significant disconnect between the role and value of education and healthy enterprising economies, with many less-educated economies growing faster than more knowledgeable ones. Moreover, theory concerning the entrepreneurial pipeline and entrepreneurial ecosystems is applied to graduate entrepreneurial intentions and aspirations. Design/methodology/approach: Using on a large-scale online quantitative survey, this study explores graduate ‘entrepreneurial intention’ in the UK and France, taking into consideration personal, social and situational factors. The results point to a number of factors that contribute to entrepreneurial intention including social background, parental occupation, gender, subject of study, and nationality. The study furthers the understanding of and contributes to the extant literature on graduate entrepreneurship. It provides an original insight into a topical and contemporary issue, raising a number of research questions for future study.Findings: For too long, students have been educated to be employees, not entrepreneurs. The study points strongly to the fact that today’s students have both willingness and intention to become entrepreneurs. However, the range of pedagogical and curriculum content does not correspond with the ambition of those who wish to develop entrepreneurial skills. There is an urgent need for directors of higher education and pedagogues to rethink their education offer in order to create a generation of entrepreneurs for tomorrow’s business world. The challenge will be to integrate two key considerations: how to create a business idea and how to make it happen practically and theoretically. Clearly, change in the education product will necessitate change in the HE business model.Research limitations/implications: The data set collected was extensive (c3500), with a focus on France and the UK. More business, engineering and technology students completed the survey than others. Further research is being undertaken to look at other countries (and continents) to test the value of extrapolation of findings. Initial results parallel those described in this paper.Practical implications: Some things can be taught, others need nurturing. Entrepreneurship involves a complex set of processes which engender individual development, and are highly personalised. Higher Education Enterprise and Teaching and Learning Strategies need to be cognisant of this, and to develop innovative and appropriate curricula, including assessment, which reflects the importance of the process as much as that of the destination.Originality/value: This work builds on an extensive literature review coupled with original primary research. The authors originate from a variety of backgrounds and disciplines, and the result is a very challenging set of thoughts, comments and suggestions that are relevant to all higher education institutions, at policy, strategy and operational levels

On the estimation of density-weighted average derivative by wavelet methods under various dependence structures

International audienceThe problem of estimating the density-weighted average derivative of a regression function is considered. We present a new consistent estimator based on a plug-in approach and wavelet projections. Its performances are explored under various dependence structures on the observations: the independent case, the $\rho$-mixing case and the $\alpha$-mixing case. More precisely, denoting $n$ the number of observations, in the independent case, we prove that it attains $1/n$ under the mean squared error, in the $\rho$-mixing case, $1/\sqrt{n}$ under the mean absolute error, and, in the $\alpha$-mixing case, $\sqrt{\ln n /n}$ under the mean absolute error. A short simulation study illustrates the theory

The Role Of Reputation In Market Entry: Evidence From French Public Procurement

This article studies the impact of reputation on market entry in public procurement. Based on the observation of a French firm with a strong reputation, we demonstrate a significant effect of the difference in public contracts won between date t-1 and date t. Our model provides empirical proof that selection of a supplier with a strong reputation does not hinder entry in public procurement nor does it prevent free competition. This result thus questions the justification for the European Union regulation that limits the use of information on past performance to select suppliers in public markets. The findings also suggest that reputation mechanisms can help reduce uncertainty during contract execution.

The degrees of freedom of the Lasso for general design matrix

In this paper, we investigate the degrees of freedom (\dof) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the \dof of the Lasso response. Namely, we show that for any given Lasso regularization parameter $\lambda$ and any observed data $y$ belonging to a set of full (Lebesgue) measure, the cardinality of the support of a particular solution of the Lasso problem is an unbiased estimator of the degrees of freedom. This is achieved without the need of uniqueness of the Lasso solution. Thus, our result holds true for both the underdetermined and the overdetermined case, where the latter was originally studied in \cite{zou}. We also show, by providing a simple counterexample, that although the \dof theorem of \cite{zou} is correct, their proof contains a flaw since their divergence formula holds on a different set of a full measure than the one that they claim. An effective estimator of the number of degrees of freedom may have several applications including an objectively guided choice of the regularization parameter in the Lasso through the \sure framework. Our theoretical findings are illustrated through several numerical simulations.Comment: A short version appeared in SPARS'11, June 2011 Previously entitled "The degrees of freedom of penalized l1 minimization

A bivariate first-order signed integer-valued autoregressive process

Bivariate integer-valued time series occur in many areas, such as finance, epidemiology, business etc. In this paper, we present bivariate autoregressive integer-valued time series models, based on the signed thinning operator. Compared to classical bivariate INAR models, the new processes have the advantage to allow for negative values for the time series and the autocorrelation functions. Strict stationarity and ergodicity of the processes are established. The moments and the autocovariance functions are determined. Some methods for estimating the model parameters are considered and the asymptotic properties of the obtained estimators are derived. Simulation experiments as well as analysis of real data sets are carried out to assess the models' performance

Une nouvelle classe de modèles auto-régressifs à valeurs entières

Rapporteur de la thèse : Pr. Christian FRANCQ, Université de Lille 3, Pr. F. Jay BREID, Colorado State University.In many practical situations we deal with integer-valued time series. The analysis of such a time series present some difficulties, namely where the analysis is based on some stochastic models. These models must reflect the integer peculiarity of the observed series. Many attempts have been made to define some models which can be used to describe integer-valued time series. Most of the proposed models are based on the thinning operator and they have the same properties as the real-valued models well-known in the literature. The aim of this thesis is to study the integer-valued autoregressive models. We introduce a new class of models based on the rounding operator. Compared to the existent models, the new class has several advantages : simple innovation structure, autoregressive coefficients with arbitrary signs, possible negative values for time series and for the autocorrelation function. We study the stationarity of the models and the strong consistency of the least squares estimator proposed to estimate the parameters. We analyze some well-known time series with the introduced models.Dans certaines situations il devient nécessaire de traiter les séries chronologiques à valeurs entières. Au premier regard, l'analyse de telle série peut présenter quelques difficultés, notamment si l'analyse est basée sur quelques modèles stochastiques. Ces modèles doivent refléter la particularité entière de la série observée. De nombreuses tentatives ont été faites pour définir des modèles qui peuvent être utilisés pour décrire les séries chronologiques à valeurs entières. La plupart des modèles proposés sont basés sur l'opérateur d'amincissement et possèdent les mêmes propriétés que les modèles à valeurs réelles bien-connus dans la littérature. L'objectif de cette thèse est d'étudier les modèles auto-régressifs à valeurs entières. Nous introduisons une nouvelle classe de modèles basés sur l'opérateur d'arrondi. Par rapport aux modèles existants, la nouvelle classe a plusieurs avantages: structure d'innovation simple, coefficients de régression avec des signes arbitraires, valeurs négatives possibles pour la série chronologiques et pour la fonction d'auto-corrélation. Nous étudions la stationnarité des modèles et la consistance forte de l'estimateur des moindres carrés proposé pour estimer les paramètres. Nous analysons quelques séries chronologiques à valeurs entières bien-connues avec les modèles introduits

A parametric study for the first-order signed integer-valued autoregressive process

In recent years, many attempts have been made to find accurate models for integer-valued times series. The SINAR (for Signed INteger-valued AutoRegressive) process is one of the most interesting. Indeed, the SINAR model allows negative values both for the series and its autocorrelation function. In this paper, we focus on the simplest SINAR(1) model under some parametric assumptions. Explicitly, we obtain the form the probability mass function of the innovation when the marginal distribution of the process is known. Moreover, we give an implicit form of the stationary distribution for a known innovation. Simulation experiments as well as analysis of real data sets are carried out to attest the models performance

A new family of bivariate discrete distributions on Z^2

In this paper we introduce a new family of bivariate discrete distributions on Z 2 , called the Rademacher(α 1 , α 2) − N 2 class. Its main feature is to generate bivariate random variables with possible negative or positive values for the covariance. This new family can also be considered as an extension (on Z^2) of some standard bivariate discrete (non negative valued) distribution