  In the Gaussian linear regression model (with unknown mean and variance), we
show that the standard confidence set for one or two regression coefficients is
admissible in the sense of Joshi (1969). This solves a long-standing open
problem in mathematical statistics, and this has important implications on the
performance of modern inference procedures post-model-selection or
post-shrinkage, particularly in situations where the number of parameters is
larger than the sample size. As a technical contribution of independent
interest, we introduce a new class of conjugate priors for the Gaussian
location-scale model.
