Statistics/Probability Theory
Constrained covariance matrix estimation in road accident modelling with Schur complements
[Estimation sous contraintes d'une matrice de covariances dans la modélisation d'accidents de la route par complements de Schur]
Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 219-222.

On considère (Y11,Y21),…,(Y1s,Y2s) une collection de s couples indépendants de vecteurs aléatoires de dimension 2r avec (r>1). On suppose que chaque couple est distribué selon une loi multinomiale dépendant à la fois d'un vecteur paramètre inconnu et d'un ensemble de données supplémentaire. On étudie l'inversion formelle de l'information de Fisher issue de ces s couples par le biais de la technique des compléments de Schur.

We consider a collection (Y11,Y21),…,(Y1s,Y2s) of s independent couples of 2r-dimensional random vector with r>1. We assume that each couple has a multinomial distribution linked to an unknown vector parameter and an extra set data. We deal with a formal inversion of a Fisher's information matrix connected to those couples using Schur complements approach.

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DOI : 10.1016/S1631-073X(03)00309-1
N'Guessan, Assi 1

1 École polytechnique universitaire de Lille et laboratoire de mathématiques appliquées: CNRS, FRE 2222, Université de Lille 1, 59655 Villeneuve d'Ascq cedex, France
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     title = {Constrained covariance matrix estimation in road accident modelling with {Schur} complements},
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N'Guessan, Assi. Constrained covariance matrix estimation in road accident modelling with Schur complements. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 219-222. doi : 10.1016/S1631-073X(03)00309-1. http://www.numdam.org/articles/10.1016/S1631-073X(03)00309-1/

[1] Aitchison, J.; Silvey, S.D. Maximum likelihood estimation of parameters subject to restraints, Ann. Math. Statist., Volume 29 (1958), pp. 813-829

[2] Crowder, M. Maximum likelihood estimation for dependent observations, J. Roy. Statist. Soc., Volume 38 (1975), pp. 45-53

[3] Crowder, M. On the constrained maximum likelihood estimation with non i.i.d. observations, Ann. Inst. Statist. Math. Part A, Volume 36 (1984), pp. 239-249

[4] Harville, D.A. Maximum likelihood approaches to variance component estimation and to related problems, J. Amer. Statist. Assoc., Volume 72 (1977) no. 358, pp. 320-340

[5] Lee, S.-Y. Constrained estimation in covariance structure analysis, Biometrika, Volume 66 (1979) no. 3, pp. 539-545

[6] N'Guessan, A.; Essai, A.; Langrand, C. Estimation multidimensionnelle des contrôles et de l'effet moyen d'une mesure de sécurité routière, Rev. Statist. Appl., Volume XLIX (2001) no. 2, pp. 83-100

[7] N'Guessan, A. On a use of Schur complements for an inverse of a constrained accident data information matrix, Pub. IRMA Lille, Volume 60 (2003) no. VI

[8] Ouellette, D.V. Schur complements and statistics, Linear Algebra Appl., Volume 36 (1981), pp. 187-295

[9] Van Eeden, C. Estimation in restricted parameter spaces – some history and some recent developments, CWI Quarterly, Volume 9 (1 and 2) (1996), pp. 69-76

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