Estimating the probability that a given vector is in the convex hull of a random sample
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00440-022-01186-1 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7466 |
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oai:localhost:PNK-74662023-04-04T02:08:03Z Estimating the probability that a given vector is in the convex hull of a random sample Satoshi, Hayakawa Terry, Lyons Harald, Oberhauser d-dimensional random vector X pn,X(θ) CC BY For a d-dimensional random vector X, let pn,X(θ) be the probability that the convex hull of n independent copies of X contains a given point θ. We provide several sharp inequalities regarding pn,X(θ) and NX(θ) denoting the smallest n for which pn,X(θ)≥1/2. As a main result, we derive the totally general inequality 1/2≤αX(θ)NX(θ)≤3d+1 , where αX(θ) (a.k.a. the Tukey depth) is the minimum probability that X is in a fixed closed halfspace containing the point θ. We also show several applications of our general results: one is a moment-based bound on NX(E[X]) , which is an important quantity in randomized approaches to cubature construction or measure reduction problem. 2023-04-04T02:08:03Z 2023-04-04T02:08:03Z 2023 Book https://link.springer.com/article/10.1007/s00440-022-01186-1 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7466 en application/pdf Springer |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
English |
| topic |
d-dimensional random vector X pn,X(θ) |
| spellingShingle |
d-dimensional random vector X pn,X(θ) Satoshi, Hayakawa Terry, Lyons Harald, Oberhauser Estimating the probability that a given vector is in the convex hull of a random sample |
| description |
CC BY |
| format |
Book |
| author |
Satoshi, Hayakawa Terry, Lyons Harald, Oberhauser |
| author_facet |
Satoshi, Hayakawa Terry, Lyons Harald, Oberhauser |
| author_sort |
Satoshi, Hayakawa |
| title |
Estimating the probability that a given vector is in the convex hull of a random sample |
| title_short |
Estimating the probability that a given vector is in the convex hull of a random sample |
| title_full |
Estimating the probability that a given vector is in the convex hull of a random sample |
| title_fullStr |
Estimating the probability that a given vector is in the convex hull of a random sample |
| title_full_unstemmed |
Estimating the probability that a given vector is in the convex hull of a random sample |
| title_sort |
estimating the probability that a given vector is in the convex hull of a random sample |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://link.springer.com/article/10.1007/s00440-022-01186-1 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7466 |
| _version_ |
1762274897170530304 |
| score |
8.893527 |