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 , 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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