Geodesic
Least squares estimator consistency: a geometric approach
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 19-45.

Voir la notice de l'article provenant de la source Library of Science

Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.
Keywords: linear models, least squares estimator, consistency, radial symmetry, generalized polar coordinates 
@article{DMPS_2006_26_1_a1,
     author = {Mexia, Jo\~ao and da Silva, Jo\~ao},
     title = {Least squares estimator consistency: a geometric approach},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {19--45},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2006},
     zbl = {1128.62029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a1/}
}
TY  - JOUR
AU  - Mexia, João
AU  - da Silva, João
TI  - Least squares estimator consistency: a geometric approach
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2006
SP  - 19
EP  - 45
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a1/
LA  - en
ID  - DMPS_2006_26_1_a1
ER  - 
%0 Journal Article
%A Mexia, João
%A da Silva, João
%T Least squares estimator consistency: a geometric approach
%J Discussiones Mathematicae. Probability and Statistics
%D 2006
%P 19-45
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a1/
%G en
%F DMPS_2006_26_1_a1
Mexia, João; da Silva, João. Least squares estimator consistency: a geometric approach. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 19-45. http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a1/

[1] P. Billingsley, Probability and Measure, (third edition), John Wiley Sons 1995.

[2] S. Cambanis, S. Huang and G. Simons, On the theory of elliptically contoured distributions, Journal of Multivariate Analysis 11 (1981), 368-385.

[3] X. Chen, Some results on consistency of LS estimates, Chin. Sci. Bull. 39 (22) (1994), 1872-1876.

[4] X. Chen, Consistency of LS estimates of multiple regression under a lower order moment condition, Sci. Chin. 38 (12) (1995), 1420-1431.

[5] X. Chen, A note on the consistency of LS estimates in linear models, Chin. Ann. Math. Ser. B, 22 (4) (2001), 471-474.

[6] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales (third edition), Springer 1997.

[7] K.L. Chung, A Course in Probability Theory (third edition), Academic Press 2001.

[8] D. Dacunha-Castelle et M. Duflo, Probabilités et Statistiques: Problèmes à Temps Fixe, Masson 1982.

[9] K. Fang, S. Kotz and K. Ng, Symmetric Multivariate and Related Distributions, Monographs on Statistics and Applied Probability 36, Chapman Hall 1990.

[10] V. Koroliouk, N. Portenko, A. Skorokhod and A. Tourbine, Aide-Mémoire de Théorie des Probabilités et de Statistique Mathématique. Mir. (1983).

[11] M. Loève, Probability Theory I (fourth edition), Springer 1977.

[12] M. Loève, Probability Theory II (fourth edition), Springer 1978.

[13] L.T. Magalhães, Álgebra Linear como Introdução á Matemática Aplicada, Texto Editora 1992.

[14] B.M. Makarov, M.G. Goluzina, A.A. Lodkin, and A.N. Podkorytov, Selected Problems in Real Analysis, American Mathematical Society 1992.

[15] J.T. Mexia, and P. Corte Real, Extension of Kolmogorov's strong law to multiple regression, Revista de Estatística, (2° quadrimestre de 2001), 24 (2001), 277-278.

[16] J.T. Mexia, P. Corte Real, M.L. Esquível, e J. Lita da Silva, Convergência do estimador dos mínimos quadrados em modelos lineares, Estatística Jubilar. Actas do XII Congresso da Sociedade Portuguesa de Estatística, Edições SPE, (2005), 455-466.

[17] J.T. Mexia e J. Lita da Silva, A consistęncia do estimador dos mínimos quadrados em domínios de atracção maximais, (to appear) 2005.

[18] J.T. Mexia and J. Lita da Silva, Least squares estimator consistency: on error stability, (to appear) 2005.

[19] J. Mingzhong, Some new results of the strong consistency of multiple regression coefficients, Proceedings of the Second Asian Mathematical Conference 1995 (Tangmanee, S. Schulz, E. eds.), World Scientific (1995), 514-519.

[20] J. Mingzhong and X. Chen, Strong consistency of least squares estimate in multiple regression when the error variance is infinite, Stat. Sin. 9 (1) (1999), 289-296.

[21] W. Pestman, Mathematical Statistics, Walter de Gruyter Berlin 1998.

[22] C.R. Rao, Linear Statistical Inference and Its Applications, (second edition), John Wiley Sons (1973).

[23] R. Schmidt, Tail dependence for elliptically contoured distributions, Mathematical Methods of Operations Research 55 (2002), 301-327.

[24] D. Williams, Probability with Martingales, Cambridge University Press, Cambridge 1991.