Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also,...

Rosenblatt's transformation has been used extensively for evaluation of model goodness-of-fit, but it only applies to models whose joint distribution is continuous. In this paper we generalize the transformation so that it applies to arbitrary probability models. The transformation is simple, but has a wide range of possible applications, providing a tool for exploratory data analysis and forma...

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...

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 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...