Sufficient conditions for the strong consistency of least squares estimator with α-stable errors

João Tiago Mexia; João Lita da Silva

Discussiones Mathematicae Probability and Statistics (2007)

  • Volume: 27, Issue: 1-2, page 27-45
  • ISSN: 1509-9423

Abstract

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Let Y i = x i T β + e i , 1 ≤ i ≤ n, n ≥ 1 be a linear regression model and suppose that the random errors e₁, e₂, ... are independent and α-stable. In this paper, we obtain sufficient conditions for the strong consistency of the least squares estimator β̃ of β under additional assumptions on the non-random sequence x₁, x₂,... of real vectors.

How to cite

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João Tiago Mexia, and João Lita da Silva. "Sufficient conditions for the strong consistency of least squares estimator with α-stable errors." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 27-45. <http://eudml.org/doc/277074>.

@article{JoãoTiagoMexia2007,
abstract = {Let $Y_\{i\} = x_\{i\}^\{T\}β + e_\{i\}$, 1 ≤ i ≤ n, n ≥ 1 be a linear regression model and suppose that the random errors e₁, e₂, ... are independent and α-stable. In this paper, we obtain sufficient conditions for the strong consistency of the least squares estimator β̃ of β under additional assumptions on the non-random sequence x₁, x₂,... of real vectors.},
author = {João Tiago Mexia, João Lita da Silva},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {linear models; least squares estimator; strong consistency; stability; least squares estimates; regression models; Marcinkiewicz-Zygmund law; undefined errors mean values},
language = {eng},
number = {1-2},
pages = {27-45},
title = {Sufficient conditions for the strong consistency of least squares estimator with α-stable errors},
url = {http://eudml.org/doc/277074},
volume = {27},
year = {2007},
}

TY - JOUR
AU - João Tiago Mexia
AU - João Lita da Silva
TI - Sufficient conditions for the strong consistency of least squares estimator with α-stable errors
JO - Discussiones Mathematicae Probability and Statistics
PY - 2007
VL - 27
IS - 1-2
SP - 27
EP - 45
AB - Let $Y_{i} = x_{i}^{T}β + e_{i}$, 1 ≤ i ≤ n, n ≥ 1 be a linear regression model and suppose that the random errors e₁, e₂, ... are independent and α-stable. In this paper, we obtain sufficient conditions for the strong consistency of the least squares estimator β̃ of β under additional assumptions on the non-random sequence x₁, x₂,... of real vectors.
LA - eng
KW - linear models; least squares estimator; strong consistency; stability; least squares estimates; regression models; Marcinkiewicz-Zygmund law; undefined errors mean values
UR - http://eudml.org/doc/277074
ER -

References

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  12. [12] T.L. Lai, H. Robbins and C.Z. Wei, Strong consistency of least squares estimates in multiple regression, Proc. Natl. Acad. Sci. USA 75 (7) (1978), 3034-3036. Zbl0386.62051
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  14. [14] J.T. Mexia, P. Corte Real, M.L. Esquível and J. Lita da Silva, Convergência do estimador dos mínimos quadrados em modelos lineares, Estaística Jubilar, Actas do XII Congresso da Sociedade Portuguesa de Estatística, Edições SPE (2005), 455-466. 
  15. [15]J.T. Mexia and J. Lita da Silva, Least squares estimator consistency: a geometric approach, Discussiones Mathematicae - Probability and Statistics 26 (1) (2006), 19-45. Zbl1128.62029
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