On approximation theorems for the Euler characteristic with applications to the bootstrap
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of con...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2021
|
| In: |
Electronic journal of statistics
Year: 2021, Jahrgang: 15, Heft: 2, Pages: 4462-4509 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/21-EJS1898 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1214/21-EJS1898 Verlag, lizenzpflichtig, Volltext: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/On-approximation-theorems-for-the-Euler-characteristic-with-applications-to/10.1214/21-EJS1898.full 
|
| Verfasserangaben: | Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 179689074X | ||
| 003 | DE-627 | ||
| 005 | 20220820154026.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 220329s2021 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1214/21-EJS1898 |2 doi | |
| 035 | |a (DE-627)179689074X | ||
| 035 | |a (DE-599)KXP179689074X | ||
| 035 | |a (OCoLC)1341458042 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Krebs, Johannes |e VerfasserIn |0 (DE-588)1137179813 |0 (DE-627)894147072 |0 (DE-576)491128266 |4 aut | |
| 245 | 1 | 0 | |a On approximation theorems for the Euler characteristic with applications to the bootstrap |c Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik |
| 264 | 1 | |c 2021 | |
| 300 | |a 48 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a First available in Project Euclid: 16 September 2021 | ||
| 500 | |a Gesehen am 29.03.2022 | ||
| 520 | |a We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of convergence in the Kantorovich-Wasserstein distance and in the Kolmogorov distance. | ||
| 650 | 4 | |a 60B10 | |
| 650 | 4 | |a 60D05 | |
| 650 | 4 | |a 60F05 | |
| 650 | 4 | |a 62F40 | |
| 650 | 4 | |a Binomial process | |
| 650 | 4 | |a bootstrap | |
| 650 | 4 | |a Čech complex | |
| 650 | 4 | |a critical regime | |
| 650 | 4 | |a Euler characteristics | |
| 650 | 4 | |a functional central limit theorem | |
| 650 | 4 | |a Normal approximation | |
| 650 | 4 | |a Poisson process | |
| 650 | 4 | |a Random geometric complexes | |
| 650 | 4 | |a smooth bootstrap | |
| 650 | 4 | |a Stochastic geometry | |
| 650 | 4 | |a topological data analysis | |
| 650 | 4 | |a weak convergence | |
| 700 | 1 | |a Roycraft, Benjamin |e VerfasserIn |0 (DE-588)1254276459 |0 (DE-627)1796890715 |4 aut | |
| 700 | 1 | |a Polonik, Wolfgang |e VerfasserIn |0 (DE-588)105122523X |0 (DE-627)785875263 |0 (DE-576)405981805 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Electronic journal of statistics |d Ithaca, NY : Cornell University Library, 2007 |g 15(2021), 2, Seite 4462-4509 |h Online-Ressource |w (DE-627)538998830 |w (DE-600)2381001-4 |w (DE-576)28134714X |x 1935-7524 |7 nnas |a On approximation theorems for the Euler characteristic with applications to the bootstrap |
| 773 | 1 | 8 | |g volume:15 |g year:2021 |g number:2 |g pages:4462-4509 |g extent:48 |a On approximation theorems for the Euler characteristic with applications to the bootstrap |
| 856 | 4 | 0 | |u https://doi.org/10.1214/21-EJS1898 |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 856 | 4 | 0 | |u https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/On-approximation-theorems-for-the-Euler-characteristic-with-applications-to/10.1214/21-EJS1898.full |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20220329 | ||
| 993 | |a Article | ||
| 994 | |a 2021 | ||
| 998 | |g 1137179813 |a Krebs, Johannes |m 1137179813:Krebs, Johannes |d 110000 |d 110200 |d 110000 |d 110400 |e 110000PK1137179813 |e 110200PK1137179813 |e 110000PK1137179813 |e 110400PK1137179813 |k 0/110000/ |k 1/110000/110200/ |k 0/110000/ |k 1/110000/110400/ |p 1 |x j | ||
| 999 | |a KXP-PPN179689074X |e 4105444603 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"title":[{"title_sort":"On approximation theorems for the Euler characteristic with applications to the bootstrap","title":"On approximation theorems for the Euler characteristic with applications to the bootstrap"}],"person":[{"given":"Johannes","family":"Krebs","role":"aut","display":"Krebs, Johannes","roleDisplay":"VerfasserIn"},{"role":"aut","roleDisplay":"VerfasserIn","display":"Roycraft, Benjamin","given":"Benjamin","family":"Roycraft"},{"given":"Wolfgang","family":"Polonik","role":"aut","roleDisplay":"VerfasserIn","display":"Polonik, Wolfgang"}],"language":["eng"],"recId":"179689074X","note":["First available in Project Euclid: 16 September 2021","Gesehen am 29.03.2022"],"type":{"media":"Online-Ressource","bibl":"article-journal"},"id":{"doi":["10.1214/21-EJS1898"],"eki":["179689074X"]},"origin":[{"dateIssuedDisp":"2021","dateIssuedKey":"2021"}],"name":{"displayForm":["Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik"]},"relHost":[{"title":[{"title":"Electronic journal of statistics","subtitle":"EJS","title_sort":"Electronic journal of statistics"}],"pubHistory":["1.2007 -"],"titleAlt":[{"title":"EJS"}],"part":{"issue":"2","pages":"4462-4509","year":"2021","extent":"48","volume":"15","text":"15(2021), 2, Seite 4462-4509"},"type":{"bibl":"periodical","media":"Online-Ressource"},"disp":"On approximation theorems for the Euler characteristic with applications to the bootstrapElectronic journal of statistics","recId":"538998830","language":["eng"],"origin":[{"dateIssuedDisp":"2007-","publisher":"Cornell University Library","dateIssuedKey":"2007","publisherPlace":"Ithaca, NY"}],"id":{"issn":["1935-7524"],"eki":["538998830"],"zdb":["2381001-4"]},"physDesc":[{"extent":"Online-Ressource"}]}],"physDesc":[{"extent":"48 S."}]} | ||
| SRT | |a KREBSJOHANONAPPROXIM2021 | ||