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2000 | 27 | 3 | 335-342
Tytuł artykułu

The two-dimensional linear relation in the errors-in-variables model with replication of one variable

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a two-dimensional linear regression model where both variables are subject to error. We discuss a model where one variable of each pair of observables is repeated. We suggest two methods to construct consistent estimators: the maximum likelihood method and the method which applies variance components theory. We study asymptotic properties of these estimators. We prove that the asymptotic variances of the estimators of regression slopes for both methods are comparable.
Słowa kluczowe
Rocznik
Tom
27
Numer
3
Strony
335-342
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-06-17
poprawiono
1999-10-25
Twórcy
  • Faculty of Management, University of Mining and Metallurgy, Gramatyka 10, 30-067 Kraków
  • Institute of Mathematics, Jagiellonian University, Reymonta 4/510, 30-059 Kraków
Bibliografia
  • J. Bartoszewicz (1989), Lectures in Mathematical Statistics, PWN, Warszawa (in Polish).
  • O. Bunke and H. Bunke (1989), Non-Linear Regression, Functional Relationships, and Robust Methods, Wiley, New York.
  • A. Czapkiewicz (1999), On estimation of parameters in the bivariate linear errors-in-variables model, Appl. Math. (Warsaw) 25, 401-410.
  • N. R. Cox (1976), The linear structural relation for several groups of data, Biometrika 63, 231-237.
  • G. R. Dolby (1976), The ultrastructural relation: A synthesis of the functional and structural relations, Biometrika 63, 39-50.
  • W. A. Fuller (1987), Measurement Error Models, Wiley, New York.
  • S. Gnot (1991), Estimation of Variance Components in Linear Models, Wyd. Naukowo-Techniczne, Warszawa (in Polish).
  • M. G. Kendall and A. Stuart (1979), The Advanced Theory of Statistics, Vol. 2, Griffin, London.
  • E. L. Lehmann (1983), Theory of Point Estimation, Wiley, New York.
  • A. Olsen, J. Seely and D. Birkes (1976), Invariant quadratic unbiased estimation for two variance components, Ann. Statist. 4, 878-890.
  • C. R. Rao and J. Kleffe (1988), Estimation of Variance Components and Applications, North-Holland Ser. Statist. Probab. 3, North-Holland, Amsterdam.
  • O. Reiersol (1950), Identifiability of a linear relation between variables which are subject to error, Econometrica 18, 575-589.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i3p335bwm
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