Optimal Experimental Designs When Some Independent Variables Are Not Subject to Control

• Published in: Journal of the American Statistical Association Vol. 99; no. 468; pp. 1190 - 1199
• Main Authors: López-Fidalgo, Jesús, Garcet-Rodríguez, Sandra A
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.12.2004; American Statistical Association; Taylor & Francis Ltd
• Subjects: Algorithm; Applications; Approximate design; Approximation; Conditionally restricted design; Covariance matrices; D-optimality; Design efficiency; Design of experiments; Determinants; Equivalence theorem; Exact sciences and technology; Experiment design; Experimental design; General topics; Inference; Integers; Linear inference, regression; Lung cancer; Lung neoplasms; Marginally restricted design; Mathematics; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Stress tests; Theory and Methods; Variables; Mixed distribution; Statistical method; Statistical regression; Regression model; Experimental design; Equivalence theorem; Iterative method; Optimal design(statistics); Algorithm; Application; Independent variable
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000001736

This article considers the problem of constructing optimal designs for regression models when the design space is a product space and some of the variables are not under the control of the practitioner. A variable that is not under control can have known values before the experiment is performed or else unknown values before the experiment is realized. The first case is briefly discussed in the literature. The aim of this work is to provide equivalence theorems for the second case and the mixture of both cases. Iterative algorithms for generating approximate optimal designs are given, and a real case of lung cancer is discussed.