The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 43, Number 5 (1972), 1383-1399.
Comparison of Translation Experiments
In this paper we treat the problem of comparison of translation experiments. The "convolution divisibility" criterion for "being more informative" by Boll (1955)  is generalized to a "$\epsilon$-convolution divisibility" criterion for $\epsilon$-deficiency. We also generalize the "convolution divisibility" criterion of V. Strassen (1965)  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) . It is shown that convergence for this distance is topologically equivalent to strong convergence of the individual probability measures up to a shift.
Ann. Math. Statist., Volume 43, Number 5 (1972), 1383-1399.
First available in Project Euclid: 27 April 2007
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Torgersen, Erik Nikolai. Comparison of Translation Experiments. Ann. Math. Statist. 43 (1972), no. 5, 1383--1399. doi:10.1214/aoms/1177692372. https://projecteuclid.org/euclid.aoms/1177692372