The elimination of nuisance parameters has classically been tackled by various ad hoc devices, and has led to a number of attemps to define partial sufficiency and ancillarity. The Bayesian approach is clearly defined. This paper examines some classical procedures in order to see when they can be given a Bayesian justification.
To study the asymptotic properties of entropy estimates, we use a unified expression, called the -entropy. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations.
A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
In a previous paper we have studied the relevant analogies between the variance, applied to a compound scheme of probability and utility, and the measure which we had defined to evaluate the unquietness for such a compound scheme.The purpose of the present note is to display the advantage exhibited by the second measure, with respect to the first one, in quantifying the uncertainty corresponding to the utilities. This advantage consists of the larger ability to distinguish among the different compound...
Neural networks with radial basis functions are considered, and the Shannon information in their output concerning input. The role of information- preserving input transformations is discussed when the network is specified by the maximum information principle and by the maximum likelihood principle. A transformation is found which simplifies the input structure in the sense that it minimizes the entropy in the class of all information-preserving transformations. Such transformation need not be unique...
Initially motivated by a practical issue in target detection via laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called minimax separation rate which corresponds to the minimal l2-distance between the signal and zero so that the detection...