Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions
| Autor: | Dominique Fourdrinier, Anis M. Haddouche, Fatiha Mezoued |
|---|---|
| Přispěvatelé: | Ecole Nationale Supérieure de Statistique et d'Economie Appliquée [Tipaza] (ENSSEA), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Numerical Analysis Pure mathematics Estimator Inverse 020206 networking & telecommunications 02 engineering and technology Type (model theory) 01 natural sciences Symmetric probability distribution law.invention 010104 statistics & probability Matrix (mathematics) Invertible matrix law 0202 electrical engineering electronic engineering information engineering 0101 mathematics Statistics Probability and Uncertainty Invariant (mathematics) [MATH]Mathematics [math] Scaling Mathematics |
| Zdroj: | Journal of Multivariate Analysis Journal of Multivariate Analysis, Elsevier, 2021, 181, pp.104680-. ⟨10.1016/j.jmva.2020.104680⟩ |
| ISSN: | 0047-259X 1095-7243 |
| Popis: | The problem of estimating the scale matrix Σ in a multivariate additive model, with elliptical noise, is considered from a decision-theoretic point of view. As the natural estimators of the form Σ ˆ a = a S (where S is the sample covariance matrix and a is a positive constant) perform poorly, we propose estimators of the general form Σ ˆ a , G = a ( S + S S + G ( Z , S ) ) , where S + is the Moore–Penrose inverse of S and G ( Z , S ) is a correction matrix. We provide conditions on G ( Z , S ) such that Σ ˆ a , G improves over Σ ˆ a under the quadratic loss L ( Σ , Σ ˆ ) = tr ( Σ ˆ Σ − 1 − I p ) 2 . We adopt a unified approach to the two cases where S is invertible and S is singular. To this end, a new Stein–Haff type identity and calculus on eigenstructure for S are developed. Our theory is illustrated with a large class of estimators which are orthogonally invariant. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect