Analysis of nearly saturated designs using composite variance estimators

Langsrud and Naes (1998) proposed forward-selection and backward-elimination strategies for the analysis of nearly saturated designs using composite variance estimators. Their variance estimators combine an estimator that is a function of the smaller sums of squares of the effect estimators (assuming effect sparsity) with an independent variance estimator based on the available error degrees of freedom. However, exact control of error rates for their stepwise methods remains an open problem. We investigate procedures that likewise use composite variance estimates but also provide exact control of error rates.