| Classical fractional design of experiment produces biased estimates of a set of parameters when aliased parameters are nonzero. In the early 1960's Ehrenfeld and Zacks constructed Randomization Procedures I and II to remove this bias from estimation of a subset of parameters of a full factorial experiment. The subset of parameters to be estimated using either of these randomization procedures must have a certain group structure. In the dissertation, we explore two estimators, the one at a time estimator and the nonorthogonal estimator, both of which remove these restrictions while producing unbiased estimates in the case of a two level experiment.{09}In later chapters we extend them to experiments with more levels per factor. The last chapter explores searching factorial models for nuisance parameters that are significant, building upon a paper by Srivastava, Designs for Searching Non-Negligible Effects. In this chapter we propose a ranking scheme, prove its fairness in searching when using a modified version of the nonorthogonal estimator, and show some simulations of its effectiveness. |
