: The investigation of a distance--based regression model, using a one--dimensional set of equally spaced points as regressor values, and p jx \Gamma yj as a distance function, leads to the study of a family of matrices which is closely related to a discrete analog of the Brownian Bridge stochastic process. We describe its eigenstructure and several properties, recovering in particular well--known results on tridiagonal Toeplitz matrices and related topics. Keywords: Distance--based regression; Centrosymmetric matrices, Orthogonal polynomials. AMS Subject classification: 62H25, 62J02 1 Introduction The distance--based regression model (Cuadras 1989; Cuadras and Arenas 1990; Cuadras et al. 1996) is an extension of the ordinary linear model which can be applied to qualitative or, in general, to mixed continuous and discrete explanatory variables, provided that a distance ffi can be defined on the set of values of these variables. A brief description of the method is as follows: Assum...

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Abstract. A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the copula corresponding to F and its univariate margins. Aulbach et al. (2012a) have shown that a copula satisfies the extreme value condition if and only if the copula is tail equivalent to a generalized Pareto copula (GPC). In this paper we propose a χ2-goodness-of-fit test in arbitrary dimension for testing whether a copula is in a certain neighborhood of a GPC. The test can be applied to stochastic processes as well to check whether the corresponding copula process is close to a generalized Pareto process. Since the p-value of the proposed test is highly sensitive to a proper selection of a certain threshold, we also present a graphical tool that makes the decision, whether or not to reject the hypothesis, more comfortable. 1.