LAMN property for hidden processes: the case of integrated diffusions

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process $X$. Our data are given by \int_0^1 X_{\frac{s+i}{n}} \dd \mu (s) for $i=0,...,n-1$ and the unknown parameter appears in the diffusion coefficient of the process $X$ only. Although the data are nor Markovian neither Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic expansion. We actually find that the asymptotic information of this model is the same one as for a usual discrete sampling of $X$

Detection of an anomalous cluster in a network

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with positive mean and unit variance, while the rest are i.i.d. standard normal. We also address surveillance settings where each sensor in the network collects information over time. The resulting model is similar, now with a time series attached to each node. We again observe the process over time and want to decide between the null, where all the variables are i.i.d. standard normal, and the alternative, where there is an emerging cluster of i.i.d. normal variables with positive mean and unit variance. The growth models used to represent the emerging cluster are quite general and, in particular, include cellular automata used in modeling epidemics. In both settings, we consider classes of clusters that are quite general, for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic, by far the most popular method in practice, achieves that same rate to within a logarithmic factor. Our results are not limited to the normal location model, but generalize to any one-parameter exponential family when the anomalous clusters are large enough.Comment: Published in at http://dx.doi.org/10.1214/10-AOS839 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Performances of a GNSS receiver for space-based applications

Space Vehicle (SV) life span depends on its station keeping capability. Station keeping is the ability of the vehicle to maintain position and orientation. Due to external perturbations, the trajectory of the SV derives from the ideal orbit. Actual positioning systems for satellites are mainly based on ground equipment, which means heavy infrastructures. Autonomous positioning and navigation systems using Global Navigation Satellite Systems (GNSS) can then represent a great reduction in platform design and operating costs. Studies have been carried out and the first operational systems, based on GPS receivers, become available. But better availability of service could be obtained considering a receiver able to process GPS and Galileo signals. Indeed Galileo system will be compatible with the current and the modernized GPS system in terms of signals representation and navigation data. The greater availability obtained with such a receiver would allow significant increase of the number of point solutions and performance enhancement. For a mid-term perspective Thales Alenia Space finances a PhD to develop the concept of a reconfigurable receiver able to deal with both the GPS system and the future Galileo system. In this context, the aim of this paper is to assess the performances of a receiver designed for Geosynchronous Earth Orbit (GEO) applications. It is shown that high improvements are obtained with a receiver designed to track both GPS and Galileo satellites. The performance assessments have been used to define the specifications of the future satellite GNSS receiver

A More Perfect Union for Whom?

Amending the federal Constitution has been instrumental in creating and developing the North American constitutional project. The difficult process embedded in Article V has been used by “The People” to expand rights and democracy, fix procedural deficiencies, and even overturn Supreme Court precedent. Yet, it is no secret that the amendment process has fallen to the wayside and that a constitutional amendment in our present age of extreme political polarization feels impossible. Our nation’s history suggests otherwise. In John F. Kowal and Wilfred U. Codrington III’s exciting and inspirational new book, they explain that interest in constitutional amendments has coincided with periods of discontent, transformational social change, and even extreme political polarization. This Piece tracks the authors’ historical and jurisprudential arguments, focusing on their claim that The People have used the Constitution to welcome marginalized groups into the nation’s political community despite their exclusion at the Founding. Although that historical claim is accurate, the campaign for a fully inclusive democracy remains unfulfilled for many. One of those groups is the people of the unincorporated territories of the United States. This Piece examines how and why the people of the unincorporated territories were never meant to be a part of our nation. It then takes the lessons from Kowal and Codrington’s book and interrogates what a constitutional amendment fully welcoming the unincorporated territories into our political fold would look like

Dual Sovereignty in the U.S. Territories

This Essay examines the emergence and application of the “ultimate source” test and sheds light on the dual sovereign doctrine’s patently colonial framework, particularly highlighting the paternalistic relationship it has produced between federal and territorial prosecutorial authorities

Dual Sovereignty in the U.S. Territories

This Essay examines the emergence and application of the ultimate source test and sheds light on the dual sovereign doctrine’s patently colonial framework, particularly highlighting the paternalistic relationship it has produced between federal and territorial prosecutorial authorities