On the influence of detection tests on deterministic parameters estimation

In non-linear estimation problems three distinct regions of operation can be observed. In the asymptotic region, the Mean Square Error (MSE) of Maximum Likelihood Estimators (MLE) is small and, in many cases,close to the Cramer-Rao bound (CRB). In the a priory performance region where the number of independent snapshots and/or the SNR are very low, the MSE is close to that obtained from the prior knowledge about the problem. Between these two extremes, there is an additional transition region where MSE of estimators deteriorates with respect to CRB. The present paper provides exemples of improvement of MSE prediction by CRB, not only in the transition region but also in the a priori region, resulting from introduction of a detection step, which proves that this renement in MSE lower bounds derivation is worth investigating

Decision Making for Rapid Information Acquisition in the Reconnaissance of Random Fields

Research into several aspects of robot-enabled reconnaissance of random fields is reported. The work has two major components: the underlying theory of information acquisition in the exploration of unknown fields and the results of experiments on how humans use sensor-equipped robots to perform a simulated reconnaissance exercise. The theoretical framework reported herein extends work on robotic exploration that has been reported by ourselves and others. Several new figures of merit for evaluating exploration strategies are proposed and compared. Using concepts from differential topology and information theory, we develop the theoretical foundation of search strategies aimed at rapid discovery of topological features (locations of critical points and critical level sets) of a priori unknown differentiable random fields. The theory enables study of efficient reconnaissance strategies in which the tradeoff between speed and accuracy can be understood. The proposed approach to rapid discovery of topological features has led in a natural way to to the creation of parsimonious reconnaissance routines that do not rely on any prior knowledge of the environment. The design of topology-guided search protocols uses a mathematical framework that quantifies the relationship between what is discovered and what remains to be discovered. The quantification rests on an information theory inspired model whose properties allow us to treat search as a problem in optimal information acquisition. A central theme in this approach is that "conservative" and "aggressive" search strategies can be precisely defined, and search decisions regarding "exploration" vs. "exploitation" choices are informed by the rate at which the information metric is changing.Comment: 34 pages, 20 figure

Extropy: Complementary Dual of Entropy

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a complementary dual function which we call "extropy." The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of distinct measures for any quantity that is not merely an event indicator. As with entropy, the maximum extropy distribution is also the uniform distribution, and both measures are invariant with respect to permutations of their mass functions. However, they behave quite differently in their assessments of the refinement of a distribution, the axiom which concerned Shannon and Jaynes. Their duality is specified via the relationship among the entropies and extropies of course and fine partitions. We also analyze the extropy function for densities, showing that relative extropy constitutes a dual to the Kullback-Leibler divergence, widely recognized as the continuous entropy measure. These results are unified within the general structure of Bregman divergences. In this context they identify half the $L_2$ metric as the extropic dual to the entropic directed distance. We describe a statistical application to the scoring of sequential forecast distributions which provoked the discovery.Comment: Published at http://dx.doi.org/10.1214/14-STS430 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Closing the technology gap?

This paper focuses on the dimensions shaping the dynamics of technology. We present a model where the knowledge stock of a country grows over time as a function of three main factors: its innovation intensity, its technological infrastructures and its human capital. The latter two variables contribute to determine the absorptive capacity of a country as well as its innovative ability. Based on this theoretical framework, we carry out an empirical analysis that investigates the dynamics of technology in a large sample of developed and developing economies in the last two-decade period, and studies its relationships with the growth of income per capita in a dynamic panel model setting. The results indicate that the cross-country distributions of technological infrastructures and human capital have experienced a process of convergence, whereas the innovative intensity is characterized by increasing polarization between rich and poor economies. Thus, while the conditions for catching up have generally improved, the increasing innovation gap represents a major factor behind the observed differences in income per capita.Growth and development; technology gap; absorptive capacity; innovation; polarization; twin-peaks