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2003 | 23 | 2 | 103-121
Tytuł artykułu

Compact hypothesis and extremal set estimators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true parameter value $\vec{β₀}^{k}$ is the sole point in ∇, strongly consistent pointwise estimators, ${ \^{\vec{βₙ}}^{k}: n ∈ ℕ }$ for $\vec{β₀}^{k}$ are derived and confidence ellipsoids for $\vec{β₀}^{k}$ centered at $\^{\vec{βₙ}}^{k}$ are obtained, as well as, strongly consistent tests. Lastly an application to binary data is presented.
Rocznik
Tom
23
Numer
2
Strony
103-121
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-11-24
poprawiono
2003-11-03
Twórcy
  • Universidade Nova de Lisboa, Departamento de Matemática, da Faculdade de Ciências e Tecnologia, Quinta da Torre, 2825-114 Monte de Caparica, Portugal
  • Universidade Nova de Lisboa, Departamento de Matemática, da Faculdade de Ciências e Tecnologia, Quinta da Torre, 2825-114 Monte de Caparica, Portugal
Bibliografia
  • [1] T. Amemiya, Advanced Econometrics, Harvard University Press 1985.
  • [2] J. Burguete, R. Gallant and G. Souza, On Unification of the Asymptotic Theory of Nonlinear Econometric Models, Econometric Reviews, 1, (1982), 151-190.
  • [3] D.R. Cox and E.J. Snell, The Analysis of Binary Data, Chapman & Hall, London, 2nd Ed., 1989.
  • [4] D. J. Finney, Probit Analysis, Cambridge University Press 1971.
  • [5] C. Gourieroux, A. Monfort and A. Trognon, Pseudo Maximum Likelihood Methods: Theory, Econometrica 52 (3), (1984).
  • [6] C. Gourieroux, A. Monfort and A. Trognon, Pseudo Maximum Likelihood Methods: Applications To Poisson Models, Econometrica 52 (3) (1984).
  • [7] R. Gallant and A. Holly, Statistical Inference in an Implicit, Nonliner, Simultaneous Equation Model in the Context of Maximum Likelihood Estimation, Econometrica 48 (1980), 697-720.
  • [8] J. Hoffman-Jorgensen, The Theory Of Analytic Sets, Aarhus Universitet, Matematisk Institut, Various Publications Series, No.10, March 1970.
  • [9] J. Hoffman-Jorgensen, Asymptotic Likelihood Theory, Aarhus Universitet, Matematisk Institut, Various Publications Series, No. 40, March 1992.
  • [10] D.E. Jennings, Judging Inference Adequacy in Logist Regression, Journal of American Statistical Association 81 (1986), 471-476.
  • [11] R. Jennrich, Asymptotic Properties of Nonlinear Least Squares Estimators, The Annals of Mathematical Statistics 40 (1969), 633-643.
  • [12] J.D. Jobson and W.A. Fuller, Least Squares Estimation When the Covariance Matrix and Parameter Vector Are Functionally Related, Journal of the American Statistical Association 75 (1980), 176-181.
  • [13] J.T. Mexia and P. Corte Real, Strong Law of Large Numbers for Additive Extremum Estimators, Discussiones Mathematicae - Probability and Statistics 21 (2002), 81-88.
  • [14] J.T. Mexia, Asymptotic Chi-squared Tests, Designs, and Log-Linear Models, Trabalhos de Investigaçäo No. 1, 1992.
  • [15] J.T. Mexia, Controlled Heteroscedasticity, Quocient Vector Spaces and F Tets for Hypothesis On Mean Vectors, Trabalhos de Investigaçäo No. 1, 1991.
  • [16] E. Malinvaud, The Consistency of Nonlinear Regressions, The Annals of Mathematical Statistics 41 (1970), 956-969.
  • [17] U. Mosco, Convergence Of Convex Sets Of Solutions Of Variational Inequalies, Advances in Mathematics 3 (1969), 510-585.
  • [18] J.T. Oliveira, Statistical Choice of Univariate Extreme Models, Statistical Distributions in Scientific Work, Taillie et al. (eds) - Reichel, Dordrecht, 6 (1980), 367-382.
  • [19] H. Scheffé, The Analysis of Variance, John Willey & Sons, New York 1959.
  • [20] A. Wald, Note On The Consistency of The Maximum Likelihood Estiamte, Annals of Mathematics and Statistics 20 (1949), 595-601.
  • [21] R.A. Wijsman, Convergence of Sequences of Convex Sets II, Transactions of American Mathematical Society 123 (1966), 32-45.
  • [22] D. Williams, Probability with Martingales, Cambridge Mathematical Textbooks 1991.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1039
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