The general setting of regression analysis is to identify a relationship between a response variable Y and one or several explanatory variables X by using a learning sample. In a prediction framework, the main assumption for predicting Y on a new sample of X observations is that the regression model Y = f(X) + ǫ is still valid. Unfortunately, this assumption is not always true in practice and t...

A family of linear models for learning in two-choice situations is considered. These models have in common the assumption that nonreward has no effect on response probability. The function r(p) that relates asymptotic probability of one of the responses to its initial probability is studied intensively. It is shown to be closely related to the total number x(p) of response alternations. The asy...

The predictive validity of personality for important life outcomes is well established, but conventional longitudinal analyses cannot rule out the possibility that unmeasured third-variable confounds fully account for the observed relationships. Longitudinal hierarchical linear models (HLM) with time-varying covariates allow each subject to serve as his or her own control, thus eliminating betw...

let $g$ be a non-abelian group and let $z(g)$ be the center of $g$. associate with $g$ there is agraph $gamma_g$ as follows: take $gsetminus z(g)$ as vertices of$gamma_g$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $gamma_g$ is called the non-commuting graph of $g$. in recent years many interesting works have been done in non-commutative graph of groups. computing the clique...

The semiparametric partially linear model allows flexible modeling of covariate effects on the response variable in regression. It combines the flexibility of nonparametric regression and parsimony of linear regression. The most important assumption in the existing methods for the estimation in this model is to assume a priori that it is known which covariates have a linear effect and which do ...

In recent years, the class of generalized linear models has gained popularity as a statistical modeling tool. This popularity is due in part to the flexibility of generalized linear models in addressing a variety of statistical problems and to the availability of software to fit the models. The SAS system provides two new tools that fit generalized linear models. The GENMOD procedure in SAS/ST...