Abstract
The information comparison ℰ A >ℰ B between two linear normal experiments ℰ A , ℰ B is studied in terms of the Loewner orderingA≤B between their defining design matricesA, B respectively. The result due toKiefer [3],Takeuchi [5]Hansen, Torgersen [1] and others is related to the comparison of certain translation invariant experiments via a reduction principle. The analysis given here completes the discussion in § 25 of [2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Hansen, O. H., Torgersen, E. N.: Comparison of linear normal experiments. Ann. of Statistics2, 367–373 (1974).
Heyer, H.: Theory of Statistical Experiments. Berlin-Heidelberg-New York: Springer. 1982.
Kiefer, J.: Optimum experimental designs. J. Royal Stat. Soc. Ser.B21, 272–319 (1959).
Swensen, A. R.: Deficiencies between linear normal experiments. Ann. of Statistics8, 1142–1155 (1980).
Takeuchi, K.: On optimal design. (In Japanese.) “Management Science”, J. Operation Res. Soc. of Japan, 23–39 (1961).
Torgersen, E. N.: Orderings of linear models. J. Stat. Planning and Inference9, 1–17 (1984).
Torgersen, E. N.: Majorization and approximate majorization for families of measures. Applications to local comparison of experiments and the theory of majorization of vectors in ℝn (Schur convexity). In: Linear Statistical Inference, pp. 259–317. Ed. by T. Caliński and W. Klonecki. Berlin-Heidelberg-New York: Springer. 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heyer, H. Bemerkungen zum Vergleich linearer normaler Experimente. Monatshefte für Mathematik 106, 9–23 (1988). https://doi.org/10.1007/BF01501485
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01501485