## The Annals of Probability

- Ann. Probab.
- Volume 6, Number 4 (1978), 688-694.

### Density-Preserving Statistics and Densities for Sample Means

#### Abstract

Among functions between manifolds those which transform probability distributions with densities to probability distributions with densities are characterised as almost submersions. As an application, conditions are given on sample size for sample means of distributions with density on Stiefel manifolds and Grassmannians to have densities.

#### Article information

**Source**

Ann. Probab., Volume 6, Number 4 (1978), 688-694.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176995490

**Digital Object Identifier**

doi:10.1214/aop/1176995490

**Mathematical Reviews number (MathSciNet)**

MR483177

**Zentralblatt MATH identifier**

0388.62047

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H10: Distribution of statistics

Secondary: 62E15: Exact distribution theory 58A10: Differential forms

**Keywords**

Density-preserving statistic almost submersion sample mean Stiefel manifold Grassmannian

#### Citation

Jupp, P. E.; Mardia, K. V. Density-Preserving Statistics and Densities for Sample Means. Ann. Probab. 6 (1978), no. 4, 688--694. doi:10.1214/aop/1176995490. https://projecteuclid.org/euclid.aop/1176995490