Statistical problems involving permutations with restricted positions
Persi W. Diaconis, Ronald Graham, Susan Holmes · Lecture notes-monograph series · 2001
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 testing extra-sensory perception with feedback.We review relevant literature on permanents, rook polynomials and complexity.The statistical applications call for new limit theorems.We prove a few of these and offer an approach to the rest via Stein's method.Tools from the proof of van der Waerden's permanent conjecture are applied to prove a natural monotonicity conjecture.