A theorem of Dolfi, Herzog, Kaplan, and Lev \cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size soluble residual is bounded from below by certain power order, inequality sharp. Inspired this result some arguments \cite{DHKL}, we establish following generalisation: if $\mathfrak{X}$ subgroup-closed formation full characteristic which does not contain all gr...

Residuals in fault detection and diagnosis are usually designed with directional or structured properties to facilitate fault isolation. With directional residuals, best isolation is achieved if the residual directions are orthogonal. In the presence of noise, the residuals are subjected to statistical testing. Testing conditions are ideal if the Fisher information matrix of the residuals is di...

In this paper, a strategy is proposed for alternative computations of the residual vectors in Krylov subspace methods, which improves the agreement of the computed residuals and the true residuals to the level of O(u)kAkkxk. Building on earlier ideas on residual replacement and on insights in the nite precision behaviour of the Krylov subspace methods, computable error bounds are derived for it...

Abstract Evaluation of document models for text based Information retrieval is crucial for developing document models that are appropriate for specific domains. Unfortunately, current document model evaluation methods for text retrieval provide no feedback, except for an evaluation score. To improve a model, we must use trial and error. In this article, we examine how we can provide feedback in...

Three types of residuals in time series models (namely ”conditional residuals”, ”unconditional residuals” and ”innovations”) are considered with regard to (i) their precise definitions, (ii) their computation after model estimation, (iii) their approximate distributions in ?nite samples, and (iv) potential applications of their properties in model diagnostic checking. Both partially-known and n...