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- CLT_normal_mixture_final_version_221118
Accepted author manuscript, 908 KB, PDF-document

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 infinity such that p/n→c ∈ [0, + ∞) when the sample covariance matrix does not need to be invertible and p/n→c ∈ [0,1) otherwise.

Original language | English |
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Pages (from-to) | 636-660 |

Number of pages | 25 |

Journal | Scandinavian Journal of Statistics |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2019 |

- large-dimensional asymptotics, normal mixtures, random matrix theory, skew normal distribution, stochastic representation

ID: 68296147