In this paper we introduce some tests for the comparison of k samples based on kernel density estimators (KDE), and we develope the Double Minimum method as a new and useful procedure for the crucial problem of bandwidth selection. We study, via Monte Carlo simulations, the statistical power of the proposed tests, as well as the impact of the smoothing degree and the performance of the Double M...

In this chapter, we propose to use a parametric multiplier approach to deriving parametric Lyapunov functions for robust stability analysis of linear systems involving uncertain parameters. This new approach generalizes the traditional multiplier approach used in the absolute stability literature where the multiplier is independent of the uncertain parameters. Our main result provides a general...

We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential W (H), we (i) find the joint distribution functions of the eigenvalues of H and H = H + V for an arbitrary fixed V both for finite matrix size N and in the “thermodynamic” N → ∞ limit; (ii) derive manypoint parametric correlation f...

The aim of this contribution is to present the concept of unipolar parametric evaluation of aggregation functions, and unify the ideas of global and local unipolar parametric evaluations. We show that several well–known parameters introduced in special classes of aggregation functions are included in this framework, and we also propose some new parameters for aggregation functions.

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...

A parametric version of the Borwein-Preiss smooth variational principle is presented, which states that under suitable assumptions on a given convex function depending on a parameter, the minimum point of a smooth convex perturbation of it depends continuously on the parameter. Some applications are given: existence of a Nash equilibrium and a solution of a variational inequality for a system o...

This paper introduces speci"cation tests of parametric mean-regression models. The null hypothesis of interest is that the parametric regression function is correctly speci"ed. The proposed tests are generalizations of the Kolmogorov}Smirnov and Cramer}von Mises tests to the regression framework. They are consistent against all alternatives to the null hypothesis, powerful against 1/Jn local al...

The possibility of employing explicitly defined functions of the observations as estimators of parametric functions in nonlinear regression analysis is explored. A general theory of best average mean square error estimation leading to explicit estimators is set forth. Such estimators are given a Bayesian interpretation as Fourier expansions of the estimator which minimizes expected posterior sq...