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A Jarque-Bera test for sphericity of a large-dimensional covariance matrix
http://hdl.handle.net/10419/73684
Title: A Jarque-Bera test for sphericity of a large-dimensional covariance matrix
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<br/>Authors: Glombek, Konstantin
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<br/>Abstract: This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X ∼ Nd(µ,Σ). This test is applicable if the sample size, n + 1, and d both go to infinity while d/n → y ∈ (0,∞), provided that the limits of tr(Σk)/d, k = 1,...,8, are finite. The main idea of this test is to check whether the empirical eigenvalue distribution of a suitably standardized sample covariance matrix obeys the semicircle law. Due to similarities of the semicircle law to the normal distribution, the proposed test statistic is of the type of the Jarque-Bera test statistic. Simulation results show that the new sphericity test outperforms the tests from the current literature for certain local alternatives if y is small.Mon, 29 Oct 2012 22:58:59 GMTA Jarque-Bera test for sphericity of a large-dimensional covariance matrix
http://hdl.handle.net/10419/73684
Title: A Jarque-Bera test for sphericity of a large-dimensional covariance matrix
<br/>
<br/>Authors: Glombek, Konstantin
<br/>
<br/>Abstract: This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X ∼ Nd(µ,Σ). This test is applicable if the sample size, n + 1, and d both go to infinity while d/n → y ∈ (0,∞), provided that the limits of tr(Σk)/d, k = 1,...,8, are finite. The main idea of this test is to check whether the empirical eigenvalue distribution of a suitably standardized sample covariance matrix obeys the semicircle law. Due to similarities of the semicircle law to the normal distribution, the proposed test statistic is of the type of the Jarque-Bera test statistic. Simulation results show that the new sphericity test outperforms the tests from the current literature for certain local alternatives if y is small.Mon, 29 Oct 2012 22:58:59 GMTFast nonparametric classification based on data depth
http://hdl.handle.net/10419/67614
Title: Fast nonparametric classification based on data depth
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<br/>Authors: Lange, Tatjana; Mosler, Karl; Mozharovskyi, Pavlo
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<br/>Abstract: A new procedure, called DD-procedure, is developed to solve the problem of classifying d-dimensional objects into q Ï 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0, 1]q . Specifically, the depth is the zonoid depth, and the algorithm is the procedure. In case of more than two classes several binary classifications are performed and a majority rule is applied. Special treatments are discussed for outsiders, that is, data having zero depth vector. The DD-classifier is applied to simulated as well as real data, and the results are compared with those of similar procedures that have been recently proposed. In most cases the new procedure has comparable error rates, but is much faster than other classification approaches, including the SVM.Sat, 29 Oct 2011 22:58:59 GMTStochastic linear programming with a distortion risk constraint
http://hdl.handle.net/10419/67613
Title: Stochastic linear programming with a distortion risk constraint
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<br/>Authors: Bazovkin, Pavel; Mosler, Karl
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<br/>Abstract: Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each risk constraint induces an uncertainty set of coefficients, which comes out to be a weighted-mean trimmed region. We consider a problem with a single constraint. Given an external sample of the coefficients, the uncertainty set is a convex polytope that can be exactly calculated. If the sample is i.i.d. from a general probability distribution, the solution of the stochastic linear program (SLP) is a consistent estimator of the SLP solution with respect to the underlying probability. An efficient geometrical algorithm is proposed to solve the SLP.Fri, 29 Oct 2010 22:58:59 GMT