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

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

Neuromyths About Neurodevelopmental Disorders: Misconceptions by Educators and the General Public

Neuromyths are commonly held misconceptions about the brain believed by both the general public and educators. While much research has investigated the prevalence of myths about the typically developing brain, less attention has been devoted to the pervasiveness of neuromyths about neurodevelopmental disorders, which have the potential to exacerbate stigma. This preregistered study investigated to what extent neuromyths about neurodevelopmental disorders (namely dyslexia, attention deficit hyperactivity disorder, autism spectrum disorders, and syndrome) are endorsed by two groups: the general public and those working in education. In an online survey, 366 members of the general public and 203 individuals working in education rated similar numbers of myths to be true, but more about neurodevelopmental disorders than general neuromyths. As the frequency of access to brain information emerged as a protective factor against endorsing myths in both populations, we argue that this problem may be addressed via provision of neuroeducational resources

Price dispersion: the case of pasta

Scopo della ricerca è indagare la possibilità di utilizzare scanner data sugli acquisti di pasta per costruire indici dei prezzi spaziali bilaterali e multilaterali utilizzando un approccio binario nella loro costruzione.The aim of our research is to explore the possibility of utilizing scanner data on pasta purchases to build bilateral and multilateral spatial price indexes, taking a binary approach in the latter.1 Pasta plays a major role in the Italian diet. Historically, pasta consumption was mainly concentrated in the Southern regions of the country but today pasta is perhaps the product most representative of the eating habits of the Italians. The range of pasta producers runs from firms of longstanding tradition (some of them mainly directed towards local markets, such as Mastromauro in Puglia) to well known international brands (such as Barilla and De Cecco). The marked increase in pasta prices over the last two years has aroused great interest, but with little focus on spatial price diversity. This study stems from the availability of an extremely detailed panel dataset (Nielsen data) on values and quantities of pasta purchased. This data was produced by the use of bar-code scanning at retail outlets and thus includes information which provides weights at an elementary level. The use of scanner data to construct price indexes is not new in literature and there is a widespread consensus on the advantages of this approach in achieving more representative indexes. Average prices (unit values) show a marked spatial price variability: even when only considering the five bestselling products, regional prices vary greatly. The paper is set out as follows: Sect. 2 provides a description of the pasta scanner dataset and briefly looks for price variability; in Sect. 3 the requirements of comparability and representativity in the case of pasta are discussed; Sect. 4 deals with the methods and formulas chosen to obtain indexes for the regional comparisons of prices; Sect. 5 shows empirical results; in Sect. 6 a brief conclusion and suggestions for future work are given

The effects of dietary insect meal from Hermetia illucens prepupae on autochthonous gut microbiota of rainbow trout (Oncorhynchus mykiss)

This study evaluated the effects of dietary insect meal from Hermetia illucens larvae on autochthonous gut microbiota of rainbow trout (Oncorhynchus mykiss). Three diets, with increasing levels of insect meal inclusion (10%, 20%, and 30%) and a control diet without insect meal were tested in a 12-week feeding trial. To analyze the resident intestinal microbial communities, the Illumina MiSeq platform for sequencing of 16S rRNA gene and QIIME pipeline were used. The number of reads taxonomically classified according to the Greengenes database was 1,514,155. Seventy-four Operational Taxonomic Units (OTUs) at 97% identity were identified. The core of adhered intestinal microbiota, i.e., OTUs present in at least 80% of mucosal samples and shared regardless of the diet, was constituted by three OTUs assigned to Propiobacterinae, Shewanella, and Mycoplasma genera, respectively. Fish fed the insect-based diets showed higher bacterial diversity with a reduction in Proteobacteria in comparison to fish fed the fishmeal diet. Insect-meal inclusion in the diet increased the gut abundance of Mycoplasma, which was attributed the ability to produce lactic and acetic acid as final products of its fermentation. We believe that the observed variations on the autochthonous intestinal microbiota composition of trout are principally due to the prebiotic properties of fermentable chitin