Eulerian polynomials have long occupied a central role in combinatorics, encapsulating critical information about permutation statistics. In their classical formulation, these polynomials encode the ...

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be ...

The rich world of permutation tests can be supplemented by a variety of applications where only some permutations are permitted. We consider two examples: testing independence with truncated data and ...