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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions

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Abstract

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime where the dimension p and the sample size n approach to in nity such that p=n ! c 2 [0;+1) when the sample covariance matrix does not need to be invertible and p=n ! c 2 [0; 1) otherwise.

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  • Bodnar, Taras & Mazur, Stepan & Parolya, Nestor, 2017. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions," Working Papers 2017:5, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2017_005
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    13. Taras Bodnar & Wolfgang Schmid, 2008. "A test for the weights of the global minimum variance portfolio in an elliptical model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 127-143, March.
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    18. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.
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    Cited by:

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    4. Javed, Farrukh & Mazur, Stepan & Ngailo, Edward, 2017. "Higher order moments of the estimated tangency portfolio weights," Working Papers 2017:10, Örebro University, School of Business.
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    7. Karlsson, Sune & Mazur, Stepan & Muhinyuza, Stanislas, 2020. "Statistical Inference for the Tangency Portfolio in High Dimension," Working Papers 2020:10, Örebro University, School of Business.

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    More about this item

    Keywords

    Normal mixtures; skew normal distribution; large dimensional asymptotics; stochastic representation; random matrix theory;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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