Statistical problems involving permutations with restricted positions. (English) Zbl 1373.62176
de Gunst, Mathisca (ed.) et al., State of the art in probability and statistics. Festschrift for Willem R. van Zwet. Papers from the symposium, Leiden, Netherlands, March 23–26, 1999. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-50-1). IMS Lect. Notes, Monogr. Ser. 36, 195-222 (2001).
Summary: 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.
For the entire collection see [Zbl 0972.00075].
For the entire collection see [Zbl 0972.00075].
MSC:
62G09 | Nonparametric statistical resampling methods |
62G10 | Nonparametric hypothesis testing |
05A05 | Permutations, words, matrices |
15A15 | Determinants, permanents, traces, other special matrix functions |