The Annals of Mathematical Statistics

Comparison of Translation Experiments

Erik Nikolai Torgersen

Full-text: Open access


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.

Article information

Ann. Math. Statist., Volume 43, Number 5 (1972), 1383-1399.

First available in Project Euclid: 27 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Torgersen, Erik Nikolai. Comparison of Translation Experiments. Ann. Math. Statist. 43 (1972), no. 5, 1383--1399. doi:10.1214/aoms/1177692372.

Export citation