A non-linear gravitational model with a multidimensional geometry and quadratic scalar curvature is considered. For certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. As a consequence, the 4–dimensional effective cosmological constant as well as the bulk cosmological constant become negative. The homogeneous and isotropic exter...

In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.

This work connects the neocybernetic theory of elastic systems to modeling of a complex industrial process. It turns out that using simple mathematics combined with multilinear tools leads to linear models that can be used for monitoring and control. As an application example, electroless nickel plating is studied.

This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. Th...

In the past several years many linear models have been proposed for analyzing two-color microarray data. As presented in the literature, many of these models appear dramatically different. However, many of these models are reformulations of the same basic approach to analyzing microarray data. This paper demonstrates the equivalence of some of these models. Attention is directed at choices in m...

The problem of estimation of the nite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter. We propose a practically fe...

In linear models with hierarchical interaction structures product type designs are shown to be D{optimal simultaneously for the whole parameter vector and for testing against any hierarchical submodel. Moreover, product type designs are also q {optimal for the highest order interactions.

ALEXANDER AUE0, LAJOS HORVÁTH1, MARIE HUŠKOVÁ2 AND PIOTR KOKOSZKA3 0Department of Mathematical Sciences, Clemson University, O-324 Martin Hall, Clemson, SC 29634, USA E-mail: [email protected] 1Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT 84112–0090, USA E-mails: [email protected] and [email protected] 2Department of Statistics, Charles University...

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models ...