Doppler Spectrum Estimation by Ramanujan Fourier Transforms

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal

On the existence of Berge's strong equilibrium

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove that most of Berge's strong games are essential.Nash equilibrium, strong Berge equilibrium, fixed point, essential games.

Exact Conditional and Unconditional Cram\`er-Rao Bounds for Near Field Localization

This paper considers the Cram\`er-Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this exact CRB can be significantly different from the one given in the literature and based on an approximate time delay expression (usually considered in the Fresnel region). This CRB derivation is then generalized by considering the exact expression of the received power profile (i.e., variable gain case) which, to our best knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization (NFL) region for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation and its developments as well as the NFL region concept through numerical simulations in different scenarios

Integration by parts formula for locally smooth laws and applications to sensitivity computations

We consider random variables of the form $F=f(V_1,...,V_n)$, where $f$ is a smooth function and $V_i,i\in\mathbb{N}$, are random variables with absolutely continuous law $p_i(y) dy$. We assume that $p_i$, $i=1,...,n$, are piecewise differentiable and we develop a differential calculus of Malliavin type based on $\partial\ln p_i$. This allows us to establish an integration by parts formula $E(\partial_i\phi(F)G)=E(\phi(F)H_i(F,G))$, where $H_i(F,G)$ is a random variable constructed using the differential operators acting on $F$ and $G.$ We use this formula in order to give numerical algorithms for sensitivity computations in a model driven by a L\'{e}vy process.Comment: Published at http://dx.doi.org/10.1214/105051606000000592 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Small, alone and poor: a merciless portrait of insolvent French firms, 2007-2010

This empirical paper investigates the path to bankruptcy for a sample of French firms in default, in particular the decision to file a petition for bankruptcy, the arbitrage between rescuing and liquidation and the effective survival. The procedure is depicted as a sequence of three steps in which judges play a crucial role as they decide whether a company is insolvent or not and determine whether an insolvent company deserves to be rescued or, on the contrary, should be liquidated, the market having the last word since the effective success depends on the capability of the firm to recover from the judicial proceedings. We test different hypotheses about the variables influencing each possibility which include i) the role of the market in the firm's health, ii) the influence of financial structures, iii) the importance of corporate governance and iv) the inherent corporate factors of probable survival. Using three linked LOGIT models, our first finding is that the probability to default depends mainly on the market. Secondly the probability to be rescued depends essentially on the financial structure. Finally, the probability for the firm to remain in business in the long term is largely influenced by the market and profitability. Our results also support the idea that governance, size and resources are the main determinants of exit from the market or success of any company.Insolvency, bankruptcy, firm default, financial indicators, size, logit models.

A Nonparametric Multivariate Control Chart Based on Data Depth

For the design of most multivariate control charts, it is assumed that the observations follow a multivariate normal distribution. In practice, this assumption is rarely satisfied. In this work, a distribution-free EWMA control chart for multivariate processes is proposed. This chart is based on equential rank of data depth measures. --