A note on the strong consistency of least squares estimates

Joǎo Lita da Silva

Discussiones Mathematicae Probability and Statistics (2009)

  • Volume: 29, Issue: 2, page 223-231
  • ISSN: 1509-9423

Abstract

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The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.

How to cite

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Joǎo Lita da Silva. "A note on the strong consistency of least squares estimates." Discussiones Mathematicae Probability and Statistics 29.2 (2009): 223-231. <http://eudml.org/doc/277049>.

@article{Joa2009,
abstract = {The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.},
author = {Joǎo Lita da Silva},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {least squares estimates; linear models; strong consistency},
language = {eng},
number = {2},
pages = {223-231},
title = {A note on the strong consistency of least squares estimates},
url = {http://eudml.org/doc/277049},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Joǎo Lita da Silva
TI - A note on the strong consistency of least squares estimates
JO - Discussiones Mathematicae Probability and Statistics
PY - 2009
VL - 29
IS - 2
SP - 223
EP - 231
AB - The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.
LA - eng
KW - least squares estimates; linear models; strong consistency
UR - http://eudml.org/doc/277049
ER -

References

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  1. [1] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales (third edition) Springer 1997. 
  2. [2] Chen Xiru, Consistency of LS estimates of multiple regression under a lower order moment condition, Sci. Chin. 38 (12) (1995), 1420-1431. Zbl0842.62054
  3. [3] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press 1985. Zbl0576.15001
  4. [4] H. Drygas, Consistency of the least squares and Gauss-Markov estimators in regression models, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17 (1971), 309-326. Zbl0204.52801
  5. [5] H. Drygas, Weak and strong consistency of the least squares estimators in regression model, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 34 (1976), 119-127. Zbl0307.62047
  6. [6] C. Gui-Jing, T.L. Lai and C.Z. Wei, Convergence systems and strong, consistency of least squares estimates in regression models, J. Multivariate Anal. 11 (1981), 319-333. Zbl0471.62065
  7. [7] C. GuiJing, Extension of Lai-Robbins-Wei's theorem, Acta Mathematicae Applicatae Sinica 1 (1) (1984), 2-7. Zbl0598.62078
  8. [8]J. Mingzhong, Some new results of the strong consistency of multiple regression coefficients, in: S. Tangmanee & E. Schulz, eds. World Scientific, Proceedings of the Second Asian Mathematical Conference 1995 (R. Nakhon 1995), 514-519. Zbl0952.62064
  9. [9] T.L. Lai, H. Robbins and C.Z. Wei, Strong consistency of least squares estimates in multiple regression II, J. Multivariate Anal. 9 (1979), 343-362. Zbl0416.62051
  10. [10] B.M. Makarov, M.G. Goluzina, A.A. Lodkin and A.N. Podkorytov, Selected Problems in Real Analysis (American Mathematical Society, Providence R.I. 1992). Zbl0858.26002
  11. [11] 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. 
  12. [12] J.T. Mexia e J. Lita da Silva, A consistência do estimador dos mínimos quadrados em domínios de atracção maximais, Ciência Estatística. Actas do XIII Congresso Anual da Sociedade Portuguesa de Estatística, Edições SPE (2006), 481-492. 
  13. [13] J.T. Mexia and J. Lita da Silva, Sufficient conditions for the strong consistency of least squares estimator with α-stable errors, Discussiones Mathematicae - Probability and Statistics 27 (2007), 27-45. 

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