## The Annals of Mathematical Statistics

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

### Comparison of Translation Experiments

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177692372

**Digital Object Identifier**

doi:10.1214/aoms/1177692372

**Mathematical Reviews number (MathSciNet)**

MR375549

**Zentralblatt MATH identifier**

0252.62004

**JSTOR**

links.jstor.org

#### Citation

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