Sharp detection of smooth signals in a high-dimensional sparse matrix with indirect observations

We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in \mathbb{Z}$. The standard deviation of our observations is \ep k^s for some \ep >0 and $s \geq 0$. We give sharp rates for the detection of a sparse submatrix of size $m \times n$ with active components. A component $(i,j)$ is said active if the sequence $\{x_{ij,k}\}_k$ have mean $\{\theta_{ij,k}\}_k$ within a Sobolev ellipsoid of smoothness $\tau >0$ and total energy $\sum_k \theta^2_{ij,k}$ larger than some r^2_\ep. Our rates involve relationships between $m,\, n, \, M$ and $N$ tending to infinity such that $m/M$, $n/N$ and \ep tend to 0, such that a test procedure that we construct has asymptotic minimax risk tending to 0. We prove corresponding lower bounds under additional assumptions on the relative size of the submatrix in the large matrix of observations. Except for these additional conditions our rates are asymptotically sharp. Lower bounds for hypothesis testing problems mean that no test procedure can distinguish between the null hypothesis (no signal) and the alternative, i.e. the minimax risk for testing tends to 1

Bayesian inference for CoVaR

Recent financial disasters emphasised the need to investigate the consequence associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting market participants' risk capital. Commonly used risk management tools fail to account for potential spillover effects among institutions because they provide individual risk assessment. We contribute to analyse the interdependence effects of extreme events providing an estimation tool for evaluating the Conditional Value-at-Risk (CoVaR) defined as the Value-at-Risk of an institution conditioned on another institution being under distress. In particular, our approach relies on Bayesian quantile regression framework. We propose a Markov chain Monte Carlo algorithm exploiting the Asymmetric Laplace distribution and its representation as a location-scale mixture of Normals. Moreover, since risk measures are usually evaluated on time series data and returns typically change over time, we extend the CoVaR model to account for the dynamics of the tail behaviour. Application on U.S. companies belonging to different sectors of the Standard and Poor's Composite Index (S&P500) is considered to evaluate the marginal contribution to the overall systemic risk of each individual institutio

Bayesian optimal adaptive estimation using a sieve prior

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.Comment: 33 pages, 2 figure

Fly-By-Wireless for Next Generation Aircraft: Challenges and Potential solutions

”Fly-By-Wireless” paradigm based on wireless connectivity in aircraft has the potential to improve efficiency and flexibility, while reducing weight, fuel consumption and maintenance costs. In this paper, first, the opportunities and challenges for wireless technologies in safety-critical avionics context are discussed. Then, the assessment of such technologies versus avionics requirements is provided in order to select the most appropriate one for a wireless aircraft application. As a result, the design of a Wireless Avionics Network based on Ultra WideBand technology is investigated, considering the issues of determinism, reliability and security

Towards an ethnography of a culturally eclectic music scene. Preserving and transforming folk music in twenty-first century England

This thesis presents an analysis of the recent transformations in the folk music scene in England. Through interviews of professional and amateur folk artists, it elicits musicians’ points of view about the music they perform and their own compositions. Adopting an ethnomusicological approach, it compares and contrasts theories of cultural globalisation with the musicians' perceptions of their position within the music scene and in relation to musical traditions in the twenty-first century. Exploring changes in music-making, collecting, and modes and contexts of transmission, this study considers how musical repertoire is exchanged, adapted and preserved within and beyond local communities through means such as archiving, pub sessions, workshops, festivals and formal tuition. From the perspectives of both artists and audiences, contemporary modes and contexts of transmission and the development of new technologies for recording, sharing and teaching music have been encouraging diverse transformations of perception, repertoire, composition and interpretation, as well as the dynamics of interaction between folk musicians. This thesis sheds light on how folk musicians’ horizons have expanded far beyond the local sphere; processes of globalisation have engendered global perspectives, new conceptualisations of what “traditional” and “folk” music are, complex identities reflected in musical hybridisation, new opportunities to access traditional and folk music, new forms of communication technology, demographical changes and cross-borders musical initiatives. The thesis demonstrates that, although the folk music scene in England might often be perceived as somewhat conservative in outlook and overshadowed by a profusion of widely disseminated contemporary popular musical products, many folk musicians have been open to transformation, adapting to new contexts and modes of transmission, embracing new communication technologies, and drawing influences from beyond the immediate local surrounding. At the same time as preserving musical heritage they have been enriching it in diverse ways to ensure its continued relevance

A test of goodness-of-fit for the copula densities

We consider the problem of testing hypotheses on the copula density from $n$ bi-dimensional observations. We wish to test the null hypothesis characterized by a parametric class against a composite nonparametric alternative. Each density under the alternative is separated in the $L_2$-norm from any density lying in the null hypothesis. The copula densities under consideration are supposed to belong to a range of Besov balls. According to the minimax approach, the testing problem is solved in an adaptive framework: it leads to a $\log\log$ term loss in the minimax rate of testing in comparison with the non-adaptive case. A smoothness-free test statistic that achieves the minimax rate is proposed. The lower bound is also proved. Besides, the empirical performance of the test procedure is demonstrated with both simulated and real data

Parametric estimation in noisy blind deconvolution model: a new estimation procedure

In a parametric framework, the paper is devoted to the study of a new estimation procedure for the inverse filter and the level noise in a complex noisy blind discrete deconvolution model. Our estimation method is a consequence of the sharp exploitation of the specifical properties of the Hankel forms. The distribution of the input signal is also estimated. The strong consistency and the asymptotic distribution of all estimates are established. A consistent simulation study is added in order to demonstrate empirically the computational performance of our estimation procedures.Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org