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International audienceIn this article, we propose an extension of integer-valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of -valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real-valued AR process can be recovered with a SINAR process, which improves INAR modeling

In this paper, we investigate the degrees of freedom (dof) of penalized 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 λ 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 [32]. We also show, by providing a simple counterexample, that although the dof theorem of [32] 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.

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. The paper aims to discuss these issues. Design/methodology/approach Using 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. Social implications The global economy, propelled by the push and pull of technology, is changing at a speed never before seen. This is having profound political, social and economic effects which necessitate fundamental change that we organise ourselves and our activities. Current models and modus operandi are proving increasingly unfit for purpose. Nurturing and encouraging agile mindsets, creativity, supporting the testing of new ideas and ways of doing things and adapting/adopting to innovation are all critical future employability factors. Our future prosperity and well-being will be dependent on creating new learning models. 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.

In this paper, we introduce a new distribution on Z 2 , which can be viewed as a natural bivariate extension of the Skellam distribution. The main feature of this distribution a possible dependence of the univariate components, both following univariate Skellam distributions. We explore various properties of the distribution and investigate the estimation of the unknown parameters via the method of moments and maximum likelihood. In the experimental section, we illustrate our theory. First, we compare the performance of the estimators by means of a simulation study. In the second part, we present two applications to a real data set and show how an improved fit can be achieved by estimating mixture distributions.

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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. Keywords Integer-valued time series • INAR models • SINAR models • Rademacher(p) − N class • Skellam distribution.