A set of Fisher information properties are presented in order to draw a parallel with similar properties of Shannon differential entropy. Already known properties are presented together with new ones, which include: (i) a generalization of mutual information for Fisher information; (ii) a new proof that Fisher information increases under conditioning; (iii) showing that Fisher information decre...

Recent petitions to list the fisher (Martes pennanti) under the Endangered Species Act have brought attention to fisher conservation. Although commercial trapping of fishers in California ended in 1946, summarizing the commercial harvest data can provide a historical perspective to fisher conservation and may indicate the prevalence of incidental fisher captures in traps set for other species. ...

1 The localization problem is fundamentally important for sensor networks. This paper studies the Cramér-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is Anchored Localization in which the estimated positions of at least 3 nodes are known in global coordinates. We show some basic invariances of the CRB in this case and derive lower and upper bo...

The year 2012 marks the 50th anniversary of the death of Sir Ronald A. Fisher, one of the two Fathers of Statistics and a Founder of the International Biometric Society (the "Society"). To celebrate the extraordinary genius of Fisher and the far-sighted vision of Fisher and Chester Bliss in organizing and promoting the formation of the Society, this article looks at the origins and growth of th...

a field survey was conducted in wukari, taraba state to assess the diversity and abundance of insect species in selected habitats (residential, open field made up of grassland and an agroecosystem). sampling were done biweekly using light, pitfall and yellow pan traps set in 3 replicates, 30 m apart. insects recovered were wet preserved in 70% ethanol except butterflies and moths. representativ...

Finite mixture distributions arise naturally in many applications including clustering and classification. Since they usually do not yield closed forms for maximum likelihood estimates (MLEs), numerical methods using the well known Fisher Scoring or Expectation-Maximization algorithms are considered. In this work, an approximation to the Fisher Information Matrix of an arbitrary mixture of mult...

We propose a modified χ-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimation error. In the case of a location parameter, we obtain new characterizations o...

Abstract. We propose a modified χ-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimation error. In the case of a location parameter, we obtain new character...

Loss of (Fisher) information, whose concept was de ned by Fisher, is one of important measures of asymptotic e ciency. Based on Fisher information, this paper studies fourth and fth order asymptotic e ciency of estimators in a curved exponential family of distributions with a structural parameter vector. In particular, we show that the bias-corrected MLE with a certain bias correction factor is...