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2007 | 27 | 1-2 | 27-45
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Kategorie tematyczne
Rocznik
Tom
27
Numer
1-2
Strony
27-45
Opis fizyczny
Daty
wydano
2007
otrzymano
2007-03-21
poprawiono
2007-11-18
Twórcy
  • Mathematics Department, Faculty of Science and Technology New, University of Lisbon, Monte da Caparica 2829-516 Caparica, Portugal
  • New University of Lisbon, Mathematics Department, Faculty of Science and Technology, Quinta da Torre, 2825-114 Monte da Caparica, Portugal
Bibliografia
  • [1] B.D.O. Anderson and J.B. Moore, On martingales and least squares linear system identification, Technical report EE7522 (1975).
  • [2] B.D.O. Anderson and J.B. Moore, A matrix Kronecker lemma, Linear Algebra and its Applications 15 (1976), 227-234.
  • [3] P. Billingsley, Probability and Measure, (third edition) John Wiley & Sons 1995.
  • [4] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer 1997.
  • [5] H. Drygas, Consistency of the least squares and Gauss-Markov estimators in regression models, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17 (1971), 309-326.
  • [6] H. Drygas, Weak and strong consistency of the least squares estimators in regression model, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 34 (1976), 119-127.
  • [7] W. Feller, An Introduction to Probability Theory and Its Applications - Volume I, (third edition) John Wiley & Sons 1968.
  • [8] W. Feller, An Introduction to Probability Theory and Its Applications - Volume II, (second edition) John Wiley & Sons 1971.
  • [9] I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen (1971).
  • [10] M. Jin, Some new results of the strong consistency of multiple regression coefficients, p. 514-519 in: 'Proceedings of the Second Asian Mathematical Conference 1995' (Tangmanee, S. & Schulz, E. eds.), World Scientific.
  • [11] M. Jin 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.
  • [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.
  • [13] 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.
  • [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]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.
  • [16] G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall 1994.
  • [17] V.V. Uchaikin and V.M. Zolotarev, Chance and Stability, Stable Distributions and Their Applications, Ultrech 1999.
  • [18] V.M. Zolotarev, One-Dimensional Stable Distributions, American Mathematical Society, Providence, R.I. 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1087
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