[Estimation sous contraintes d'une matrice de covariances dans la modélisation d'accidents de la route par complements 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.
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.
Accepté le :
Publié le :
Assi N'Guessan 1
@article{CRMATH_2003__337_3_219_0, author = {Assi N'Guessan}, title = {Constrained covariance matrix estimation in road accident modelling with {Schur} complements}, journal = {Comptes Rendus. Math\'ematique}, pages = {219--222}, publisher = {Elsevier}, volume = {337}, number = {3}, year = {2003}, doi = {10.1016/S1631-073X(03)00309-1}, language = {en}, }
Assi N'Guessan. Constrained covariance matrix estimation in road accident modelling with Schur complements. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 219-222. doi : 10.1016/S1631-073X(03)00309-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00309-1/
[1] Maximum likelihood estimation of parameters subject to restraints, Ann. Math. Statist., Volume 29 (1958), pp. 813-829
[2] Maximum likelihood estimation for dependent observations, J. Roy. Statist. Soc., Volume 38 (1975), pp. 45-53
[3] 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] Maximum likelihood approaches to variance component estimation and to related problems, J. Amer. Statist. Assoc., Volume 72 (1977) no. 358, pp. 320-340
[5] Constrained estimation in covariance structure analysis, Biometrika, Volume 66 (1979) no. 3, pp. 539-545
[6] 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] 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] Schur complements and statistics, Linear Algebra Appl., Volume 36 (1981), pp. 187-295
[9] Estimation in restricted parameter spaces – some history and some recent developments, CWI Quarterly, Volume 9 (1 and 2) (1996), pp. 69-76
- Analytical existence of solutions to a system of nonlinear equations with application, Journal of Computational and Applied Mathematics, Volume 234 (2010) no. 1, pp. 297-304 | DOI:10.1016/j.cam.2009.12.026 | Zbl:1201.65080
- Impact of a road safety layout on the severity of crashes, Journal de la Société Française de Statistique Revue de Statistique Appliquée, Volume 149 (2008) no. 3, pp. 23-41 | Zbl:1455.62228
- An estimation method of the average effect and the different accident risks when modelling a road safety measure: A simulation study, Computational Statistics and Data Analysis, Volume 51 (2006) no. 2, pp. 1260-1277 | DOI:10.1016/j.csda.2005.09.002 | Zbl:1157.62525
- A Schur complement approach for computing subcovariance matrices arising in a road safety measure modelling, Journal of Computational and Applied Mathematics, Volume 177 (2005) no. 2, pp. 331-345 | DOI:10.1016/j.cam.2004.09.023 | Zbl:1072.65009
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