Abstract
D. Basu gave a striking bivariate normal example, N2(0, 0, 1, 1, ρ) with an unknown correlation coefficient ρ, − 1 < ρ < 1, where the jointly sufficient statistic (X1, X2) consists of two ancillary statistics X1, X2. We exhibit examples of ancillary statistics involving both X1, X2 followed by other variations. A situation is highlighted where a jointly minimal sufficient statistic (X1, X2) is made up of ancillary statistics X1, X2. Then, we illustrate a concrete multivariable full model which questions the customary practice of contrasting non-constant reduced models via deletion of one covariate at-a-time.
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