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A family of matrices, the discretized Brownian Bridge and distancebased regression
, 1997
"... : The investigation of a distancebased regression model, using a onedimensional 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 stochasti ..."
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: The investigation of a distancebased regression model, using a onedimensional 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 wellknown results on tridiagonal Toeplitz matrices and related topics. Keywords: Distancebased regression; Centrosymmetric matrices, Orthogonal polynomials. AMS Subject classification: 62H25, 62J02 1 Introduction The distancebased 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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, 2014
"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has ..."
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This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has
TESTING FOR A δNEIGHBORHOOD OF A GENERALIZED PARETO COPULA
"... Abstract. A multivariate distribution function F is in the maxdomain 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 ..."
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Abstract. A multivariate distribution function F is in the maxdomain 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 χ2goodnessoffit 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 pvalue 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.