## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

# On an Inequality of Hoeffding and Rosén

Jan Lanke
Scandinavian Journal of Statistics
Vol. 1, No. 2 (1974), pp. 84-86
Stable URL: http://www.jstor.org/stable/4615556
Page Count: 3

You can always find the topics here!

Topics: Statism, Random sampling, Mathematical inequalities, Random variables

#### Select the topics that are inaccurate.

Cancel
If X̄ and Ȳ denote the averages in two equally large samples obtained through simple random sampling with and without replacement, respectively, Hoeffding has proved that $\text{E}[\text{g}(\overline{\text{Y}}]\leq \text{E}[\text{g}(\overline{\text{X}}]$ for any convex function g while Rosén has shown that the same inequality holds also in the more general case when the X-sample has been drawn by any symmetric sampling design. Letting Z̄ denote the average of the values of the distinct units in the X-sample, we will show that $\text{E}[\text{g}(\overline{\text{Y}}]\leq \text{E}[\text{g}(\overline{\text{Z}}]\leq \text{E}[\text{g}(\overline{\text{X}}]$ holds under Rosén's assumptions.