Open Access
October, 1972 Comparison of Translation Experiments
Erik Nikolai Torgersen
Ann. Math. Statist. 43(5): 1383-1399 (October, 1972). DOI: 10.1214/aoms/1177692372


In this paper we treat the problem of comparison of translation experiments. The "convolution divisibility" criterion for "being more informative" by Boll (1955) [2] is generalized to a "$\epsilon$-convolution divisibility" criterion for $\epsilon$-deficiency. We also generalize the "convolution divisibility" criterion of V. Strassen (1965) [13] to a criterion for "$\varepsilon$-convolution divisibility." It is shown, provided least favorable "$\varepsilon$-factors" can be found, how the deficiencies actually may be calculated. As an application we determine the increase of information--as measured by the deficiency--contained in an additional number of observations for a few experiments (rectangular, exponential, multivariate normal, one way layout). Finally we consider the problem of convergence for the pseudo distance introduced by LeCam (1964) [8]. It is shown that convergence for this distance is topologically equivalent to strong convergence of the individual probability measures up to a shift.


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Erik Nikolai Torgersen. "Comparison of Translation Experiments." Ann. Math. Statist. 43 (5) 1383 - 1399, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0252.62004
MathSciNet: MR375549
Digital Object Identifier: 10.1214/aoms/1177692372

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 5 • October, 1972
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