## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 2 (1976), 423-430.

### On Invariance and Randomization in Fractional Replication

J. N. Srivastava, B. L. Raktoe, and H. Pesotan

#### Abstract

This paper generalizes the results of Paik and Federer (1970), Ehrenfeld and Zacks (1961) and Zacks (1963, 1964) regarding invariance and randomization in fractional replication. It is shown that (i) the characteristic roots of the information matrix of a design in the general factorial relative to an admissible vector of effects remain invariant under a permutation of levels; (ii) the unbiased estimation of a linear function of an admissible vector of effects can be obtained under equal probability randomization. In addition some applications of the results are indicated.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 2 (1976), 423-430.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343421

**Digital Object Identifier**

doi:10.1214/aos/1176343421

**Mathematical Reviews number (MathSciNet)**

MR395094

**Zentralblatt MATH identifier**

0328.62048

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62K15: Factorial designs

Secondary: 62J05: Linear regression

**Keywords**

Factorial fractional replicate information matrix level permutations admissible effects randomization linear estimation

#### Citation

Srivastava, J. N.; Raktoe, B. L.; Pesotan, H. On Invariance and Randomization in Fractional Replication. Ann. Statist. 4 (1976), no. 2, 423--430. doi:10.1214/aos/1176343421. https://projecteuclid.org/euclid.aos/1176343421