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Estimation of scatter matrix based on i.i.d. sample from elliptical distributions

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Abstract

In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samplesx (1),...x (n) are i.i.d. andx (1)∼EC p(μ,Σ,f). With respect to entropy and quadratic losses, we obtain the best estimator ofΣ having the formα S x as well as having the formT xΔTx′, whereS x,Tx andΔ are given in the text, and obtain the minimax estimator ofΣ and the best equivariant estimator ofΣ with respect to the triangular transformations groupLT +(p) (the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.

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Authors and Affiliations

  1. Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080, Beijing, China

    Fang Kaitai

  2. Hong Kong Baptist University, Kowloon, Hong Kong

    Fang Kaitai

  3. Prob. Lab., Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080, Beijing, China

    Li Runze

Authors
  1. Fang Kaitai
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  2. Li Runze
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Additional information

This work is supported by the National Natural Science Foundation of China and Hong Kong UPGC Grant.

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Fang, K., Li, R. Estimation of scatter matrix based on i.i.d. sample from elliptical distributions. Acta Mathematicae Applicatae Sinica 11, 405–412 (1995). https://doi.org/10.1007/BF02007178

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  • DOI: https://doi.org/10.1007/BF02007178

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