Symmetry and Unimodality in Linear Inference

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 under symmetry and unimodality of errors. Normal-theory approximate tests are seen to exhibit monotone power in certain classes of symmetric unimodal errors.