Behavior of elemental sets in regression

Elemental sets are used to produce trial estimates b of the regression coefficients β. If b0 minimizes ∥b-β∥ among all elemental fits b, then ∥b0-β∥=OP(n-1), regardless of the criterion used. For any estimator bA, ∥bA-β∥ is at best OP(n-1/2). Hence restricting fits to elemental introduces asymptotically negligible error.