For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...

In this paper, an imprecise data classification is considered using new version of Fisher discriminator, namely interval Fisher. In the conventional formulation of Fisher, elements of within-class scatter matrix (related to covariance matrix between clusters) and between-class scatter matrix (related to covariance matrix of centers of clusters) have single values; but in the interval Fisher, th...

The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information in a set of data and to calculate the lower bound (Cramér−Rao bound) of the variance for estimates such as maximum likelihood and to conduct score tests. (It is also of interest to note that other measures of information in the data are useful in pr...

We ask whether or not the saddlepoint property holds. for robust M-estimation of scale, in gross-errors and Kolmogorov neighbourhoods of certain distributions. This is of interest since the saddlepoint property implies the minimax property that the supremum of the asymptotic variance of an M-estimator is minimized by the maximum likelihood estimator for that member of the distributional class w...

 Abstract: A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochas...

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points . The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this ...

This paper examines the influence of parametric uncertainties on the optimal sensor placement methodologies for the modal analysis of a truss bridge. Four classical sensor location methodologies are employed: two based on the Fisher information matrix and the other two based on energy matrix rank optimization. Young's modulus, mass density and cross sectional dimensions are considered as uncert...

Suppose that k series, all having the same autocorrelation function, are observed in parallel at n points in time or space. From a single series of moderate length, the autocorrelation paramater β can be estimated with limited accuracy, so we aim to increase the information by formulating a suitable model for the joint distribution of all series. Three Gaussian models of increasing complexity a...

Fisher-Hartwig asymptotics refers to the large n form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the o...

For the widely used multilayer perceptrons (MLPs), there exist singularities in parameter space where Fisher information matrix (FIM) degenerates on these subspaces. The seriously influence learning dynamics of MLPs which have attracted many researchers’ attentions. As FIM plays key role investigating singular MLPs, it is very important to obtain analytical form FIM. In this paper, for bipolar ...