Details
| Original language | English |
|---|---|
| Pages (from-to) | 155-182 |
| Number of pages | 28 |
| Journal | METRIKA |
| Volume | 87 |
| Issue number | 2 |
| Early online date | 12 May 2023 |
| Publication status | Published - Feb 2024 |
Abstract
We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.
Keywords
- Asymptotics, Boundary theory, Copulas, Exchangeability, Markov chains, Pattern frequencies, Permutations, Ranks
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: METRIKA, Vol. 87, No. 2, 02.2024, p. 155-182.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ranks, copulas, and permutons
AU - Grübel, R.
N1 - Funding Information: Over the years, discussions with Ludwig Baringhaus, Steve Evans, Julian Gerstenberg, Klaas Hagemann, Anton Wakolbinger and Wolfgang Woess were instrumental for my understanding of many of the above concepts. I am also grateful to the referees for their helpful and encouraging comments.
PY - 2024/2
Y1 - 2024/2
N2 - We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.
AB - We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.
KW - Asymptotics
KW - Boundary theory
KW - Copulas
KW - Exchangeability
KW - Markov chains
KW - Pattern frequencies
KW - Permutations
KW - Ranks
UR - http://www.scopus.com/inward/record.url?scp=85159275871&partnerID=8YFLogxK
U2 - 10.1007/s00184-023-00908-2
DO - 10.1007/s00184-023-00908-2
M3 - Article
AN - SCOPUS:85159275871
VL - 87
SP - 155
EP - 182
JO - METRIKA
JF - METRIKA
SN - 0026-1335
IS - 2
ER -