Minimax Estimation in Linear Models

• Autorzy: Hilmar Drygas

Warianty tytułu

Estymacja minimax w modelach liniowych

• Języki publikacji: EN

Abstrakty

EN

We consider the linear model у= Xβ + σε, Εε = 0, Εεε' = Ι_n. We give a review of the problems involved with the determination of the Best Linear Estimator of β in this model. (short original abstract)

Rozważamy model liniowy у= Xβ + σε, Εε = 0, Εεε' = Ι_n. Podajemy przegląd problemów związanych z determinacją Najlepszego Liniowego Estymatora Minimaxowego β w tym modelu. (skrócony abstrakt oryginalny)

Słowa kluczowe

EN

Estimation; Linear models

PL

Estymacja; Modele liniowe

• Czasopismo: Acta Universitatis Lodziensis. Folia Oeconomica
• Rocznik: 1993
• Tom: 132
• Strony: 99--110

Twórcy

autor

Hilmar Drygas

• University of Kassel

Bibliografia

• Dennis J. E. (jr), Schnabel (1983): Numerical methods for Unconstrained Optimization and Nonllneare Equations, Prontlce-Hnll, New Jeraey.
• Drygas H. (1985): Minimax Prediction in Linear Models, [in:] Linear Statistical Inference (T. Celiński and W. Klonecki, eds.), Proceedings of the International Conference held at Poznań. Poland, June 4-8, 1984, p. 48-60.
• Drygas H. (1988): A note on Minimax-Estimation in Regression Modele with Affine Restrictions, "Kasseler Mathematische Schriften", 2/88 (June).
• Drygas H., Linear Minimax-Estimation in Linear Models with affine and Ellipsoidal Restrictions, 1991 (in:) Computational Statistics and Data Analysis.
• Girkо V. L. (1988): Multidimensional Statistical Analysis, Wyča Szkola, Kiew (Russian): an English translation, (Kluwer, Doredrecht; 1993) Is in preparation.
• Göpfert A. (1973): Mathematische Optimierung in allgemeinen Vektorräumen, BSC B. G. Teubner Verlagsgesellschaft, Leipzig.
• Hoffmann K. (1979): Characterization of Minimax Linear Estimators ln Linear Regression, Math. Operationsf. u. Statistik, Series Statistics, 10, p. 19-26.
• Läuter H. (1975): A minimax Linear Estimator for Linear Parameters Under Restrictions ln Form of Inequalities, Math. Operationsf. u. Statistik, Ser. B, Statistics, 6, p. 689-695.
• Stahlecker P. (1985): A priori Information und Minimax-Schätzung im Linearen Regressions- modeli, Habilitationsschrift an der Universität Hannover, appeared also in 1987 as No. 108 of Mathematical Systems ln Economics, Frankfurt am Main.
• Stahleclcer P. and Lauterbach J. (1989): Approximate Lineare Minimax Estimation in Regression Analysis with Ellipsoidal Constraints, "Communications in Statistics) Theory and Methods", 18, no. 8, p. 2755-2784.
• Stahlecker P. and Trenkler G. (1988): Full and Partial Minimax Estimation with additional Linear Constraints, "Linear Algebra and its Applications", 111, p. 279-292.