Least squares estimator consistency: a geometric approach

João Tiago Mexia; João Lita da Silva

Discussiones Mathematicae Probability and Statistics (2006)

  • Volume: 26, Issue: 1, page 19-45
  • ISSN: 1509-9423

Abstract

top
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.

How to cite

top

João Tiago Mexia, and João Lita da Silva. "Least squares estimator consistency: a geometric approach." Discussiones Mathematicae Probability and Statistics 26.1 (2006): 19-45. <http://eudml.org/doc/277028>.

@article{JoãoTiagoMexia2006,
abstract = {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.},
author = {João Tiago Mexia, João Lita da Silva},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {linear models; least squares estimator; consistency; radial symmetry; generalized polar coordinates},
language = {eng},
number = {1},
pages = {19-45},
title = {Least squares estimator consistency: a geometric approach},
url = {http://eudml.org/doc/277028},
volume = {26},
year = {2006},
}

TY - JOUR
AU - João Tiago Mexia
AU - João Lita da Silva
TI - Least squares estimator consistency: a geometric approach
JO - Discussiones Mathematicae Probability and Statistics
PY - 2006
VL - 26
IS - 1
SP - 19
EP - 45
AB - 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.
LA - eng
KW - linear models; least squares estimator; consistency; radial symmetry; generalized polar coordinates
UR - http://eudml.org/doc/277028
ER -

References

top
  1. [1] P. Billingsley, Probability and Measure, (third edition), John Wiley & Sons 1995. 
  2. [2] S. Cambanis, S. Huang and G. Simons, On the theory of elliptically contoured distributions, Journal of Multivariate Analysis 11 (1981), 368-385. Zbl0469.60019
  3. [3] X. Chen, Some results on consistency of LS estimates, Chin. Sci. Bull. 39 (22) (1994), 1872-1876. Zbl0827.62056
  4. [4] X. Chen, Consistency of LS estimates of multiple regression under a lower order moment condition, Sci. Chin. 38 (12) (1995), 1420-1431. Zbl0842.62054
  5. [5] X. Chen, A note on the consistency of LS estimates in linear models, Chin. Ann. Math. Ser. B, 22 (4) (2001), 471-474. Zbl0984.62014
  6. [6] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales (third edition), Springer 1997. 
  7. [7] K.L. Chung, A Course in Probability Theory (third edition), Academic Press 2001. 
  8. [8] D. Dacunha-Castelle et M. Duflo, Probabilités et Statistiques: Problèmes à Temps Fixe, Masson 1982. Zbl0535.62003
  9. [9] K. Fang, S. Kotz and K. Ng, Symmetric Multivariate and Related Distributions, Monographs on Statistics and Applied Probability 36, Chapman & Hall 1990. 
  10. [10] V. Koroliouk, N. Portenko, A. Skorokhod and A. Tourbine, Aide-Mémoire de Théorie des Probabilités et de Statistique Mathématique. Mir. (1983). 
  11. [11] M. Loève, Probability Theory I (fourth edition), Springer 1977. Zbl0359.60001
  12. [12] M. Loève, Probability Theory II (fourth edition), Springer 1978. 
  13. [13] L.T. Magalhães, Álgebra Linear como Introdução á Matemática Aplicada, Texto Editora 1992. 
  14. [14] B.M. Makarov, M.G. Goluzina, A.A. Lodkin, and A.N. Podkorytov, Selected Problems in Real Analysis, American Mathematical Society 1992. 
  15. [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. [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. [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. [18] J.T. Mexia and J. Lita da Silva, Least squares estimator consistency: on error stability, (to appear) 2005. Zbl1128.62029
  19. [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. Zbl0952.62064
  20. [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. Zbl0913.62024
  21. [21] W. Pestman, Mathematical Statistics, Walter de Gruyter Berlin 1998. 
  22. [22] C.R. Rao, Linear Statistical Inference and Its Applications, (second edition), John Wiley & Sons (1973). Zbl0256.62002
  23. [23] R. Schmidt, Tail dependence for elliptically contoured distributions, Mathematical Methods of Operations Research 55 (2002), 301-327. Zbl1015.62052
  24. [24] D. Williams, Probability with Martingales, Cambridge University Press, Cambridge 1991. Zbl0722.60001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.