## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 41, Number 2 (1970), 369-375.

### A Randomized Procedure of Saturated Main Effect Fractional Replicates

#### Abstract

Ehrenfeld and Zacks [2] presented randomized procedures for regular fractions and Zacks [3], [4] showed that an unbiased estimator of a given parameter vector in the saturated fractional replicate case exists only if one randomizes over all possible designs of a certain structure. In this paper, a similar method to the Randomized Procedure I in their paper is given for the saturated irregular main effect fractional replicates and an unbiased estimator of the main effect parameter vector is presented. Prior to this presentation, an invariant property of the information matrix is investigated. The explicit expression of the variance of the estimator is a remaining problem.

#### Article information

**Source**

Ann. Math. Statist., Volume 41, Number 2 (1970), 369-375.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697077

**Digital Object Identifier**

doi:10.1214/aoms/1177697077

**Mathematical Reviews number (MathSciNet)**

MR258202

**Zentralblatt MATH identifier**

0235.62018

**JSTOR**

links.jstor.org

#### Citation

Paik, U. B.; Federer, W. T. A Randomized Procedure of Saturated Main Effect Fractional Replicates. Ann. Math. Statist. 41 (1970), no. 2, 369--375. doi:10.1214/aoms/1177697077. https://projecteuclid.org/euclid.aoms/1177697077