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## Discussiones Mathematicae Probability and Statistics

2001 | 21 | 2 | 81-88
Tytuł artykułu

### Strong law of large numbers for additive extremum estimators

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Extremum estimators are obtained by maximizing or minimizing a function of the sample and of the parameters relatively to the parameters. When the function to maximize or minimize is the sum of subfunctions each depending on one observation, the extremum estimators are additive. Maximum likelihood estimators are extremum additive whenever the observations are independent. Another instance of additive extremum estimators are the least squares estimators for multiple regressions when the usual assumptions hold. A strong law of large numbers is derived for additive extremum estimators. This law requires only the existence of first order moments and may be of interest in connection with maximum likelihood estimators, since the usual assumption that the observations are identically distributed is discarded.
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EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
81-88
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-06-10
poprawiono
2001-08-26
Twórcy
autor
• Universidade Nova de Lisboa, Departamento de Matemática, da Faculdade de Ciências e Tecnologia, Quinta da Torre, 2825-114 Monte de Caparica
autor
• Universidade Nova de Lisboa, Departamento de Matemática, da Faculdade de Ciências e Tecnologia, Quinta da Torre, 2825-114 Monte de Caparica
Bibliografia
• [1] N. Bac Van, Strong convergence of least squares estimates in polynomial regression with random explanatory variables, Acta Mathematica Vietnamica 23 (2) (1998), 195-205.
• [2] N. Bac Van, Strong convergence of least squares estimates in polynomial regression with random explanatory variables, Acta Mathematica Vietnamica 19 (1) (1994), 111-137.
• [3] J. Galambos, Advanced Probability Theory, Marcel Dekker 1988.
• [4] J.T. Mexia and P.C. Real, Extension of Kolmogorov's strong law to multiple regression, 23rd European Meeting of Statisticians, Funchal (Madeira Island), August 13-18 2001, Revista de Estatística, 2 Quadrimestre de 2001, 277-278.
• [5] D. Williams, Probability with Martingales, Cambridge Mathematical Textbooks 1991.
• [6] S. Zacks, The Theory of Statistical Inference, John Wiley 1971.
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Bibliografia
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