Semiparametric CRB and Slepian-Bangs formulas for Complex Elliptically Symmetric Distributions

The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data. Moreover, the CES distributions has been widely recognized as a valuable and general model to statistically describe the non-Gaussian behaviour of datasets originated from a wide variety of physical measurement processes. The paper is divided in two parts. In the first part, a closed form expression of the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint estimation of complex mean vector and complex scatter matrix of a set of CES-distributed random vectors is obtained by exploiting the so-called \textit{Wirtinger} or $\mathbb{C}\mathbb{R}$-\textit{calculus}. The second part deals with the derivation of the semiparametric version of the Slepian-Bangs formula in the context of the CES model. Specifically, the proposed Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM) for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a CES-distributed vector in the presence of unknown, nuisance, density generator. Furthermore, we show how to exploit the derived SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for Direction of Arrival (DOA) estimation under a random signal model assumption. Simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: substantial text overlap with arXiv:1807.08505, arXiv:1807.0893

Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust $M$-estimator of mean vector and scatter matrix when no a-priori information on the density generator is available. A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$-estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on Signal Processin

How Wood Fuels\u2019 Quality Relates to the Standards: A Class-Modelling Approach

The quality requirements of wood biofuels are regulated by a series of harmonized international standards. These standards define the technical parameter limits that influence the quality of solid biomass as a fuel. In 2014 the European reference standard for solid biofuel was replaced by the International ISO standard. In the case of wood chips, the main difference between the European and International standards is the definition of particle size distribution classes. In this context, this study analyses the quality of wood chips and its variation over the years according to the \u201cformer\u201d (EN 14691-4) and \u201cin force\u201d (ISO 17225-4) standards. A Soft Independent Modelling of Class Analogy (SIMCA) model was built to predict the best quality of wood chips and to clarify the relationship between quality and standard parameters, time and changes in the standard regulations. The results show that, compared to the EN standards, classification with the ISO standards increases the samples belonging to the best quality classes and decreases the not classified samples. Furthermore, all the SIMCA models have a high sensitivity (>90%), reflect the differences introduced to the quality standards and are therefore suitable for monitoring the quality of wood chips and their changes

The Impact of the EU Development Policy in Indian Higher Education: the EDUREFOM Project and the Socio-economic Impact of the Fourth Industrial Revolution as a Case Study

The fourth industrial revolution is expected to deeply affect the Indian socio-economic trends. Higher education is gradually acquiring significance in the agenda of development and cooperation policies. In the last decade, the European Union has supported Indian higher education institutions to enhance their role in the development of the country. The Erasmus+ has been revised to intertwine the internal and external dimensions, embedding goals related to social, political and economic spheres. To pursue this goal, under the Erasmus+ Capacity Building in Higher Education action, the EU has allowed Indian universities to ideate and develop projects addressing local needs and global challenges. Through case study and participant observation, the article assesses the EU's action in India for cooperation development initiatives engaging the Indian higher education sector. The research findings have been instrumental in delivering targeted recommendations to European policymakers to enhance the impact of the EU developmental cooperation policy in India and the EU-India relations tout court

PATHOLOGICAL NARCISSISM

Thus, having become very famous in the cities of Aonia, the one (Tiresias) gave irrefutable responses to those who consulted him. The first to test the authenticity of his words was the blue Lirìope, whom Cefiso had one day pushed into a bend in his current, imprisoned in the waves and raped. When she got pregnant, the beautiful nymph gave birth to a child who aroused love from birth, and called him Narcissus. Asked if the little boy would see the distant days of late old age, the soothsayer replied: "If he doesn\u27t know himself." For a long time the prediction seemed meaningless, but then the outcome of things, the type of death and the strange passion confirmed it. "The Metamorphosis" (Ovidio)