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Subject: Covariance matrix × WGL Institute: WIAS ×

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Now showing 1 - 2 of 2
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    Bayesian inference for spectral projectors of the covariance matrix
    (Ithaca, NY : Cornell University Library, 2018) Silin, Igor; Spokoiny, Vladimir
    Let X1,…,Xn be an i.i.d. sample in Rp with zero mean and the covariance matrix Σ∗. The classical PCA approach recovers the projector P∗J onto the principal eigenspace of Σ∗ by its empirical counterpart ˆPJ. Recent paper [24] investigated the asymptotic distribution of the Frobenius distance between the projectors ∥ˆPJ−P∗J∥2, while [27] offered a bootstrap procedure to measure uncertainty in recovering this subspace P∗J even in a finite sample setup. The present paper considers this problem from a Bayesian perspective and suggests to use the credible sets of the pseudo-posterior distribution on the space of covariance matrices induced by the conjugated Inverse Wishart prior as sharp confidence sets. This yields a numerically efficient procedure. Moreover, we theoretically justify this method and derive finite sample bounds on the corresponding coverage probability. Contrary to [24, 27], the obtained results are valid for non-Gaussian data: the main assumption that we impose is the concentration of the sample covariance ˆΣ in a vicinity of Σ∗. Numerical simulations illustrate good performance of the proposed procedure even on non-Gaussian data in a rather challenging regime.
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    On the Simes inequality in elliptical models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Bodnar, Taras; Dickhaus, Thorsten
    We provide necessary and sufficient conditions for the validity of the inequality of Simes (1986) in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statistics is violated. Since our sufficient conditions require nonnegativity of correlation coefficients between test statistics, we also develop exact tests for vectors of correlation coefficients.