On the Nature of Saturated 2-Factor Quadratic Response Designs for Unbiased Estimation of Quadratic Effects Parameters

By : Sobita Sapam, Nripes Kumar Mandal, Bikas K Sinha

Page No: 49-62

Abstract
We contemplate an experimental situation which deals with a 2-factor quadratic response involving, in its model expectation, the mean term, both the linear  effects parameters, and both the quadratic effects parameters as well as the product term parameter. We assume the errors to be homoscedastic and uncorrelated. Our intention is to conduct a saturated design [SD] - using a subset of six distinct but suitably chosen design points in an appropriately defined factor space. Further to this, we wish to achieve maximum precision in joint estimation of the last three [quadratic effects] parameters. It is known beforehand that these three effect(s)/interaction(s) are likely to be non-negligible. We examine the flexibility to the extent that an experimenter can make a choice of an SD, retaining information on the three remaining effects/interactions as well. We use the D-optimality criterion and deal with a continuous design set-up. At the end, we also discuss about A-optimality criterion.

Authors :
Bikas K Sinha
Indian Statistical Institute, Kolkata.

Sobita Sapam
Manipur University, Canchipur [Imphal], Manipur.

Nripes Kumar Mandal
Calcutta University, Kolkata.

DOI: DOI-https://doi.org/10.32381/IAPQRT.2021.45.01-02.4