Nonlinarity of Boolean functions and hyperelliptic curves

We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersingular curves of genus 2. We give some criterion for a vectorial function not to be almost perfect nonlinear

Too much consensus could be harmful : measuring the degree of implementation of the Washington consensus and its impact on economic growth

In this paper, we construct a unique quantitative measure of the depth and pace of all aspects of IFI programs — the Washington consensus index (WCI), and we investigate their whole impact on economic growth. Two main conclusions emerge. Firstly, among observed countries, those who come up to Consensus expectations maintain a relatively high degree of government involvement. Secondly, when combined with usual explanatory variables, WCI presents a significant non-linear relation with the probability of getting a higher growth than others get. Thus, it seems that a “too fast” and/or a “too far” implementation of IFI programs, especially in regard of deregulation and monetary orthodoxy, can harm growth in developing countries. L’objectif de ce papier est double. Dans un premier temps, nous construisons un indicateur quantitatif mesurant le degré d’application des programmes des IFI – l’indicateur du consensus de Washington – pour ensuite évaluer par ce biais l’impact de ces programmes sur la croissance économique d’un certain nombre de pays en développement. Deux principales conclusions apparaissent. D’une part, parmi les pays observés, ceux qui répondent le mieux aux attentes des IFI le font en maintenant un certain degré d’implication de l’Etat. D’autre part, une fois introduit dans un modèle usuel de croissance, notre indicateur présente une relation non-linéaire avec la probabilité de bénéficier d’un taux de croissance économique supérieur à celui des autres pays. Ainsi, il apparaît qu’une mise en œuvre trop rapide ou trop importante des programmes des IFI, particulièrement en termes de déréglementation et de politique monétaire, nuit à la croissance des pays en développement. (Full text in english)

On recursive estimation for time varying autoregressive processes

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise estimates is shown to be minimax in $\beta$-Lipschitz classes for $0<\beta\leq1$. For $1<\beta\leq 2$, this property no longer holds. This can be seen by using an asymptotic expansion of the estimation error. A bias reduction method is then proposed for recovering the minimax rate.Comment: Published at http://dx.doi.org/10.1214/009053605000000624 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrade when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1-D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators

On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semi-parametric framework introduced by Robinson and his co-authors for estimating the memory parameter of a (possibly) non-stationary process. As an application, we obtain minimax upper bounds for the log-scale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.Comment: to appear in the Journal of Time Series Analysi

The Distribution of Earnings under Monopsonistic/polistic Competition

Recent empirical contributions in labor economics suggest that individual firms face upward sloping labor supplies. We rationalize this by assuming that idiosyncratic non-pecuniary conditions interact with money wages in workers’ decisions to work for specific firms. Likewise, firms supply differentiated goods in response to differences in consumer tastes. Hence, firms are price-makers and wage-setters. By combining monopolistic and monopsonistic competition, our setting encapsulates general equilibrium interactions between the two markets. The equilibrium involves double exploitation of labor. Compared to the competitive outcome, the high-productive workers are overpaid under free entry, whereas the low-productive workers are underpaid. In the same vein, capital-owners receive a premium, whereas workers are exploited.wage dispersion, worker heterogeneity, monopsonistic competition, monopolistic competition, labor exploitation

Impact of PWM strategies on RMS current of the DC-link Voltage Capacitor of a dual-three phase drive

The major drawback of usual dual three-phase AC machines, when supplied by a Voltage Source Inverter (VSI), is the occurrence of extra harmonic currents which circulate in the stator windings causing additional losses and constraints on the power component. This paper compares dedicated Pulse Width Modulation (PWM) strategies used for controlling a dual three phase Permanent Magnet Synchronous machine supplied by a six-leg VSI. Since the application is intended for low-voltage (48V) mild-hybrid automotive traction, an additional major constraint arises: the compactness of the drive related to the size of the DC-bus capacitor. Thus, the PWM strategy must be chosen by taking into consideration its impact on both, the motor and the RMS value of DC-bus current

A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series

We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet Estimator" of the memory parameter $d$. This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales or on a range which becomes infinite with the sample size. We show that the estimator is consistent and rate optimal if $X$ is a linear process and is asymptotically normal if $X$ is Gaussian