Given function values on a domain D0 , possibly with noise, we examine the possibility of extending the function to a larger domain D,D0 ⊂ D. In addition to smoothness at the boundary of D0 , the extension to D \ D0 should also inherit behavioral trends of the function on D0 , such as growth and decay or even oscillations. The approach chosen here is based upon the framework of linear models, u...

It is a well-known theorem in linear models that the idempotency of a matrix is a sufficient and necessary condition for a quadratic form in normal variates to have a chi-square distribution, but its proofs in the early literature were incorrect or incomplete. Driscoll (1999) provided an improved proof, and this article presents a simple proof. More importantly, we establish and prove a general...

In this paper, a new voting system model is introduced as a linear transformation model. The size of compartmental populations in each political group corresponding to every voted subject, the population weights, the weighted votes policy against each political group, the “Yes” and “No” rates, the “No” rejection policy and the “Yes” increase policy are the inputs / outputs of the introduced lin...

an algebraic construction for constant dimension subspace codes is called orbit code. it arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. in particular orbit codes of a singer subgroup of the general linear group has investigated recently. in this paper, we consider the normalizer of a singer subgroup of the general linear group a...

The process of globalization has continued to generate controversy on its impact on groups that are vulnerable to poverty. In this respect, there is evidence that farmers in most developing countries are increasingly vulnerable to poverty due to a number of reasons. One possible reason could be the limited access to the technologies that assist farmers in improving their production and later in...

Goldstein (1986) describes the analysis of the multilevel mixed effects linear model with random coefficients, where the variance and covariance components have a nested structure across levels. The purpose of the present note is to show how a simple extension to the formulae in that paper can accommodate cross-classifications of the components within any level of the nesting, thus enabling qui...

Multiplicative interaction models, such as Goodman's (1981) RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are suitable only for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of interaction effects in generalized linear models with...

In this paper we study the identiiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspeciied. Identiiability in such models does not mean uniqueness of parameters but rather uniqueness of the set of predictions of interest to the investigator. For example, predicting the eeects of c...