The use of conditional cutoffs in a forward selection procedure
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 16 (8) , 2227-2241
- https://doi.org/10.1080/03610928708829502
Abstract
Using a forward selection procedure for selecting the best subset of regression variables involves the calculation of critical values (cutoffs) for an F-ratio at each step of a multistep search process. On dropping the restrictive (unrealistic) assumptions used in previous works, the null distribution of the F-ratio depends on unknown regression parameters for the variables already included in the subset. For the case of known σ, by conditioning the F-ratio on the set of regressors included so far and also on the observed (estimated) values of their regression coefficients, we obtain a forward selection procedure whose stepwise type I error does not depend on the unknown (nuisance) parameters. A numerical example with an orthogonal design matrix illustrates the difference between conditional cutoffs, cutoffs for the centralF-distribution, and cutoffs suggested by Pope and Webster.Keywords
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