Partially linear models with local kernel regression are popular non-parametric techniques. However, bandwidth selection in the models is a puzzling topic that has been addressed in literature with the use of undersmoothing and regular smoothing. In an attempt to address the strategy of bandwidth selection, we review profile-kernel based and backfitting methods for partially linear models, and ...

The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known ([PQ99] and [Pau03]) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We st...

The mental process of comparing numbers is shown to follow the principles of Relative Judgment Theory. Martingale predictions of the theory are confirmed in an extensive study of numerical comparisons using the Method of Symmetric Differences. The theory is then used as a tool to reveal the Psychonumeric Function relating psychological difference to numerical difference. This function transform...

Recently there have two different effective methods proposed by Kanzow et al. in [19] and [21], respectively, which commonly use the Fischer-Burmeister (FB) function to recast the mixed complementarity problem (MCP) as a constrained minimization problem and a nonlinear system of equations, respectively. They all remark that their algorithms may be improved if the FB function is replaced by othe...