Distribution-free results beyond Gauss-Markov theory are found under weak assumptions regarding the errors. Symmetry, unimodality, and location-scale families are studied in estimation; nonstandard versions of Gauss-Markov results are given; and distribution-free confidence sets are tightened...

It is shown that randomization applies in repeated measurements whenever the F-test applies in the analysis. Contrary to common practice, randomization otherwise invalidates the use of Hotelling's T2 and Box's approximate test, and it presents difficulties in testing that dispersion matrices...

Let be a Studentizing transformation of the type T(Y) = [nu]A'Y/||B'Y||, and let GM(n) consist of scale mixtures of Gaussian laws on [bumpy equals]k; 1 [less-than-or-equals, slant] k [less-than-or-equals, slant] n[bumpy equals]. It is shown that GM(n) is closed under T(·). Concentration...

Suppose that experimental designs have comparable A-efficiencies for estimation, the choice among designs then depending on their comparative D-efficiencies. Using the theory of majorization, it is shown that designs having greater D-efficiencies are more ill-conditioned, using condition numbers...

Anomalies are cited in the use of subset regression diagnostics. Two leverage diagnostics are unified through canonical leverages. Other diagnostics relate one-to-one with the R-Fisher statistic, supporting exact but equivalent tests at level [alpha]. Three distance diagnostics exhibit ad hoc...

Effects of augmenting or deleting sets of design points are studied using principal components of the predictive dispersion at those points. The affected linear parameters are then given explicitly in terms of design points and coefficients defining the principal predictors. In addition to...

Let [mu](· ; [Sigma], G1) and [mu](· ; [Omega], G2) be elliptically contoured measures on k centered at 0, having scale parameters ([Sigma], [Omega]) and radial cdf's (G1, G2). Elliptical measures vm(·) and vM(·), depending on ([Sigma], [Omega], G1, G2), are constructed such that...