Confidence regions for level sets
This paper discusses a universal approach to the construction of confidence regions for level sets {h(x)≥0}⊂Rq of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate ĥn of h. The approach provides finite sample upper and...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
13 August 2013
|
| In: |
Journal of multivariate analysis
Year: 2013, Jahrgang: 122, Pages: 202-214 |
| ISSN: | 1095-7243 |
| DOI: | 10.1016/j.jmva.2013.07.017 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1016/j.jmva.2013.07.017 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0047259X13001498 
|
| Verfasserangaben: | Enno Mammen, Wolfgang Polonik |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1567845223 | ||
| 003 | DE-627 | ||
| 005 | 20220814063914.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 180130s2013 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.jmva.2013.07.017 |2 doi | |
| 035 | |a (DE-627)1567845223 | ||
| 035 | |a (DE-576)497845229 | ||
| 035 | |a (DE-599)BSZ497845229 | ||
| 035 | |a (OCoLC)1340986356 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Mammen, Enno |d 1955- |e VerfasserIn |0 (DE-588)170668606 |0 (DE-627)060788658 |0 (DE-576)13153159X |4 aut | |
| 245 | 1 | 0 | |a Confidence regions for level sets |c Enno Mammen, Wolfgang Polonik |
| 264 | 1 | |c 13 August 2013 | |
| 300 | |a 13 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 30.01.2018 | ||
| 520 | |a This paper discusses a universal approach to the construction of confidence regions for level sets {h(x)≥0}⊂Rq of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate ĥn of h. The approach provides finite sample upper and lower confidence limits. This leads to generic conditions under which the constructed confidence regions achieve a prescribed coverage level asymptotically. The construction requires an estimate of quantiles of the distribution of supΔn|ĥn(x)−h(x)| for appropriate sets Δn⊂Rq. In contrast to related work from the literature, the existence of a weak limit for an appropriately normalized process {ĥn(x),x∈D} is not required. This adds significantly to the challenge of deriving asymptotic results for the corresponding coverage level. Our approach is exemplified in the case of a density level set utilizing a kernel density estimator and a bootstrap procedure. | ||
| 650 | 4 | |a Kernel density estimation | |
| 650 | 4 | |a Level sets | |
| 650 | 4 | |a Nonparametric curve estimation | |
| 650 | 4 | |a Smooth bootstrap | |
| 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 Journal of multivariate analysis |d [Amsterdam] : Elsevier, 1971 |g 122(2013), Seite 202-214 |h Online-Ressource |w (DE-627)267328141 |w (DE-600)1469773-7 |w (DE-576)103373233 |x 1095-7243 |7 nnas |a Confidence regions for level sets |
| 773 | 1 | 8 | |g volume:122 |g year:2013 |g pages:202-214 |g extent:13 |a Confidence regions for level sets |
| 856 | 4 | 0 | |u http://dx.doi.org/10.1016/j.jmva.2013.07.017 |x Verlag |x Resolving-System |3 Volltext |
| 856 | 4 | 0 | |u http://www.sciencedirect.com/science/article/pii/S0047259X13001498 |x Verlag |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20180130 | ||
| 993 | |a Article | ||
| 994 | |a 2013 | ||
| 998 | |g 105122523X |a Polonik, Wolfgang |m 105122523X:Polonik, Wolfgang |p 2 |y j | ||
| 998 | |g 170668606 |a Mammen, Enno |m 170668606:Mammen, Enno |p 1 |x j | ||
| 999 | |a KXP-PPN1567845223 |e 2994565331 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"id":{"eki":["1567845223"],"doi":["10.1016/j.jmva.2013.07.017"]},"origin":[{"dateIssuedDisp":"13 August 2013","dateIssuedKey":"2013"}],"name":{"displayForm":["Enno Mammen, Wolfgang Polonik"]},"relHost":[{"disp":"Confidence regions for level setsJournal of multivariate analysis","note":["Gesehen am 20.06.2023"],"type":{"media":"Online-Ressource","bibl":"periodical"},"recId":"267328141","language":["eng"],"pubHistory":["1.1971 - 102.2011; Vol. 103.2012 -"],"part":{"pages":"202-214","year":"2013","extent":"13","text":"122(2013), Seite 202-214","volume":"122"},"titleAlt":[{"title":"Multivariate analysis"},{"title":"JMVA"}],"title":[{"title":"Journal of multivariate analysis","subtitle":"JMVA","title_sort":"Journal of multivariate analysis"}],"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"publisherPlace":"[Amsterdam] ; Orlando, FL","publisher":"Elsevier ; Academic Press","dateIssuedKey":"2001","dateIssuedDisp":"2001-"}],"id":{"issn":["1095-7243"],"zdb":["1469773-7"],"eki":["267328141"]}}],"physDesc":[{"extent":"13 S."}],"title":[{"title":"Confidence regions for level sets","title_sort":"Confidence regions for level sets"}],"person":[{"roleDisplay":"VerfasserIn","display":"Mammen, Enno","role":"aut","family":"Mammen","given":"Enno"},{"roleDisplay":"VerfasserIn","display":"Polonik, Wolfgang","role":"aut","family":"Polonik","given":"Wolfgang"}],"language":["eng"],"recId":"1567845223","type":{"bibl":"article-journal","media":"Online-Ressource"},"note":["Gesehen am 30.01.2018"]} | ||
| SRT | |a MAMMENENNOCONFIDENCE1320 | ||