Geometry of linear and quadratic estimation in a normal linear model with singular variance-covariance matrix

• Autorzy: Stępniak Cz.
• Języki publikacji: EN

Abstrakty

EN

Many statistical problems, among others those involving restrains on parameters, lead to the models with singular variance-covariance matrix. It is shown that the problems can be reduced to the same problems in the standard linear model.

Słowa kluczowe

EN

linear model; singular variance-covariance matrix; linear estimation; quadratic estimation; geometry of inference

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 3
• Strony: 639--645
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Stępniak Cz.

• Institute of Mathematics, Pedagogical University of Rzeszów, Rejtana 16A, 35-310 Rzeszów, Poland
• Institute of Applied Mathematics, Agricultural University of Lublin, Akademicka 13, 20-934 Lublin, Poland

Bibliografia

• [1] S. Kołodziejczyk, On an important class of statistical hypotheses, Biometrika 27 (1935), 161-190.
• [2] H. Scheffé, Analysis of Variance, Wiley, New York, 1959.
• [3] J. Seely, A complete sufficient statistic for the linear model under normality and singular covariance matrix, Comm. Statist. Theory Methods A 7 (1978), 1465-1473.
• [4] C. Stępniak, Admissible linear estimators in mixed linear models, J. Multivariate Anal. 31 (1989), 90-106.
• [5] C. Stępniak, S. G. W a n g and C. F. J. W u , Comparison of linear experiments with known covariances, Ann. Statist. 12 (1984), 358-365.
• [6] E. Torgersen, Comparison of Statistical Experiments, Cambridge Univ. Press, Cambridge, 1991.