In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We demonstrate how this assumption can allow us to fit higher...

we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...

We study the behavior of the conjugate-gradient method for solving a set of linear equations, where the matrix is symmetric and positive definite with one set of eigenvalues that are large and the remaining are small. We characterize the behavior of the residuals associated with the large eigenvalues throughout the iterations, and also characterize the behavior of the residuals associated with ...

At the finest scale of our coarse-to-fine alignment strategy, we require an alignment technique which performs well given large tile sizes but a very small search radius. In this context, techniques such as our previously-described fast subpixel L2 alignment, or even simpler techniques such as phase correlation [Kuglin and Hines 1975] are outperformed by a well-implemented brute-force procedure...

The most often used approaches to obtaining and using residuals in applied work with time series models, are unified and documented with both partially-known and new features. Specifically, three different types of residuals, namely "conditional residuals", "unconditional residuals" and "innovations", are considered with regard to (i) their precise definitions, (ii) their computation in practic...

Large quantities of animal residuals are produced every day. In some cases, these residuals can be recycled by application to land in its raw form. In other cases, the residuals must be treated to reduce its strength in order to recycle that material on land. Large production units for producing animals are on the rise, thus no longer allowing recycling on land as a viable option. For processin...

Abstract Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. In this paper, we propose a GP Regression model with a latent variab...

Fault Detection and Isolation (FDI) problems are here considered for linear systems with faults and disturbances. We design a set of observer-based residuals, in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals allows fault isolation. We are interested in obtaining a transfer function from faults to residuals with eith...

In the presence of generalized conditional heteroscedasticity (GARCH) in the residuals of a vector error correction model (VECM), maximum likelihood (ML) estimation of the cointegration parameters has been shown to be efficient. On the other hand, full ML estimation of VECMs with GARCH residuals is computationally difficult and may not be feasible for larger models. Moreover, ML estimation of V...

The aim of nuclear safeguards is to ensure that special nuclear material is used for peaceful purposes. Historically, nuclear material accounting (NMA) has provided the quantitative basis for monitoring for nuclear material loss or diversion, and process monitoring (PM) data is collected by the operator to monitor the process. PM data typically support NMA in various ways, often by providing a ...