Asymptotic robustness of Kelly's GLRT and Adaptive Matched Filter detector under model misspecification

A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models cannot be achieved in many practical applications. In all these cases, it is advisable to use a robust decision test, i.e. a test whose statistic preserves (at least asymptotically) the same probability density function (pdf) for a suitable set of possible input data models under the null hypothesis. Building upon the seminal work of Kent (1982), in this paper we investigate the impact of the model mismatch in a recurring HT problem in radar signal processing applications: testing the mean of a set of Complex Elliptically Symmetric (CES) distributed random vectors under a possible misspecified, Gaussian data model. In particular, by using this general misspecified framework, a new look to two popular detectors, the Kelly's Generalized Likelihood Ration Test (GLRT) and the Adaptive Matched Filter (AMF), is provided and their robustness properties investigated.Comment: ISI World Statistics Congress 2017 (ISI2017), Marrakech, Morocco, 16-21 July 201

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

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

The strategic role of the corporate social responsibility and circular economy in the cosmetic industry

In the literature, circular economy (CE) and corporate social responsibility (CSR) are increasingly interconnected concepts. Turon at al. (2016) consider CE the guidelines of conduct for designing and developing good CSR strategies. In particular, the corporate management philosophy needs to be translated into mandatory CSR reports that better frames circular economy objectives by identifying and communicating actions to achieve sustainable development goals. The purpose of this paper is to explore a number of CSR reports in order to understand if cosmetic multinationals' (MNC) nonfinancial reporting is focused on the concept of circular economy and if CSR reports ensure an adequate level of disclosure to circular strategies. Moreover, the paper highlights the advantages that arise by converging the concepts of CSR and CE. The originality of this paper lies on providing evidence on "how" MNC are implementing a circular model. This paper contributes to our understanding on the relation between CSR and CE; it assesses the state of the art of circular strategies in MNC and proposes a consolidation of the concept of CE in terms of sustainable strategic and managerial practices communicated to the market by CSR reports. Moreover, it brings MNC to a better understanding of the ways to communicate their new circular business model. The analysis reveals a good level of attention by MNC to circularity in drafting their CSR reports that in many cases are able to describe objectives and actions that embrace multiple dimensions

Circular economy and corporate social responsibility in the agricultural system: Cases study of the Italian agri-food industry

The persistent exploitation of natural resources and the consequent use of consumption are driving global food demand with the result that agricultural activity is becoming less and less environmentally friendly. The circular economy (CE) can become a valid alternative, inserting the economic-agricultural system into the harmonic process of material circulation. The corporate social responsibility (CSR) model is particularly interesting not only because of the ethical dimension of the company but also as a factor of strategic business improvement that combines the concepts of CSR and CE as possible solutions for developing sustainable business processes. The objective of the work is to highlight a detailed framework of how the small and medium-sized enterprises (SMEs) of the Italian agri-food industry can provide an ade-quate level of communication, circular strategies and social responsibility practices. The research methodology is based on a qualitative multiple study conducted on a sample of nine companies in the Italian territory. The study highlights the attention of companies on the issues of the CE for the achievement of the set sustainable objectives and the attention to CSR and CE practices. The work has several implications. It provides a further understanding of CSR and CE policies as enabling factors for the development of sustainable organizational performance in agriculture. Moreover, it better investigates the relationship between CSR and the CE. Finally, it analyses the SMEs state of the art in the CE field and strengthens the concept of CE by analysing corporate practices consistent with sustainability reports

Scaling up MIMO Radar for Target Detection

This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the »classical' temporal domain, we propose to explore the spatial dimension (i.e., number of antennas M) to derive asymptotic results for the detector. Specifically, we assume no a priori knowledge of the statistics of the autoregressive data generating process and propose to use a mispecified Wald-type detector, which is shown to have an asymptotic χ-squared distribution as M → ∞. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results are used to validate the asymptotic analysis in the finite system regime. It turns out that, for the considered scenario, the asymptotic performance is closely matched already for M ≥ 50

Massive MIMO radar for target detection

Since the seminal paper by Marzetta from 2010, the Massive MIMO paradigm in communication systems has changed from being a theoretical scaled-up version of MIMO, with an infinite number of antennas, to a practical technology. Its key concepts have been adopted in the 5G new radio standard and base stations, where 64 fully-digital transceivers have been commercially deployed. Motivated by these recent developments, this paper considers a co-located MIMO radar with MT transmitting and MR receiving antennas and explores the potential benefits of having a large number of virtual spatial antenna channels N=MTMR. Particularly, we focus on the target detection problem and develop a robust Wald-type test that guarantees certain detection performance, regardless of the unknown statistical characterization of the disturbance. Closed-form expressions for the probabilities of false alarm and detection are derived for the asymptotic regime N→∞. Numerical results are used to validate the asymptotic analysis in the finite system regime with different disturbance models. Our results imply that there always exists a sufficient number of antennas for which the performance requirements are satisfied, without any a-priori knowledge of the disturbance statistics. This is referred to as the Massive MIMO regime of the radar system