FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3091837215> ?p ?o ?g. }

• W3091837215 abstract "In the past decades, the central limit theorem (CLT) has been generalized to non-Euclidean data spaces. Some years ago, it was found that for some random variables on the circle, the sample Frechet mean fluctuates around the population mean asymptotically at a scale $n^{-tau}$ with exponent $tau < 1/2$ with a non-normal distribution if the probability density at the antipodal point of the mean is $frac{1}{2pi}$. The author and his collaborator recently discovered that $tau = 1/6$ for some random variables on higher dimensional spheres. In this article we show that, even more surprisingly, the phenomenon on spheres of higher dimension is qualitatively different from that on the circle, as it depends purely on geometrical properties of the space, namely its curvature, and not on the density at the antipodal point. This gives rise to the new concept of geometrical smeariness. In consequence, the sphere can be deformed, say, by removing a neighborhood of the antipodal point of the mean and gluing a flat space there, with a smooth transition piece. This yields smeariness on a manifold, which is diffeomorphic to Euclidean space. We give an example family of random variables with 2-smeary mean, i.e. with $tau = 1/6$, whose range has a hole containing the cut locus of the mean. The hole size exhibits a curse of dimensionality as it can increase with dimension, converging to the whole hemisphere opposite a local Frechet mean. We observe smeariness in simulated landmark shapes on Kendall pre-shape space and in real data of geomagnetic north pole positions on the two-dimensional sphere." @default.
• W3091837215 created "2020-10-15" @default.
• W3091837215 creator A5049480942 @default.
• W3091837215 date "2019-08-12" @default.
• W3091837215 modified "2023-09-27" @default.
• W3091837215 title "Geometrical Smeariness -- A new Phenomenon of Fr'echet Means" @default.
• W3091837215 cites W1657323942 @default.
• W3091837215 cites W1879832876 @default.
• W3091837215 cites W1942440616 @default.
• W3091837215 cites W1974553802 @default.
• W3091837215 cites W1990265918 @default.
• W3091837215 cites W1997352815 @default.
• W3091837215 cites W2008494137 @default.
• W3091837215 cites W2009995300 @default.
• W3091837215 cites W2021087958 @default.
• W3091837215 cites W2027729304 @default.
• W3091837215 cites W2034649075 @default.
• W3091837215 cites W2040079214 @default.
• W3091837215 cites W2040125300 @default.
• W3091837215 cites W2044974898 @default.
• W3091837215 cites W2072931016 @default.
• W3091837215 cites W2080795841 @default.
• W3091837215 cites W2089846098 @default.
• W3091837215 cites W2096374577 @default.
• W3091837215 cites W2098497817 @default.
• W3091837215 cites W2105041874 @default.
• W3091837215 cites W2109409043 @default.
• W3091837215 cites W2111309001 @default.
• W3091837215 cites W2117807326 @default.
• W3091837215 cites W2128325826 @default.
• W3091837215 cites W2130617294 @default.
• W3091837215 cites W2140286913 @default.
• W3091837215 cites W2142999993 @default.
• W3091837215 cites W218887819 @default.
• W3091837215 cites W2296866626 @default.
• W3091837215 cites W2950691275 @default.
• W3091837215 cites W2963261057 @default.
• W3091837215 cites W2963505506 @default.
• W3091837215 cites W2964223277 @default.
• W3091837215 cites W2964586256 @default.
• W3091837215 cites W2971800164 @default.
• W3091837215 cites W2981811430 @default.
• W3091837215 cites W2982355266 @default.
• W3091837215 cites W2987028841 @default.
• W3091837215 cites W3021977414 @default.
• W3091837215 cites W3098043740 @default.
• W3091837215 cites W939702425 @default.
• W3091837215 hasPublicationYear "2019" @default.
• W3091837215 type Work @default.
• W3091837215 sameAs 3091837215 @default.
• W3091837215 citedByCount "5" @default.
• W3091837215 countsByYear W30918372152019 @default.
• W3091837215 countsByYear W30918372152020 @default.
• W3091837215 countsByYear W30918372152021 @default.
• W3091837215 crossrefType "posted-content" @default.
• W3091837215 hasAuthorship W3091837215A5049480942 @default.
• W3091837215 hasConcept C105795698 @default.
• W3091837215 hasConcept C111030470 @default.
• W3091837215 hasConcept C114614502 @default.
• W3091837215 hasConcept C134306372 @default.
• W3091837215 hasConcept C186450821 @default.
• W3091837215 hasConcept C192939610 @default.
• W3091837215 hasConcept C202444582 @default.
• W3091837215 hasConcept C2524010 @default.
• W3091837215 hasConcept C33923547 @default.
• W3091837215 hasConcept C70943382 @default.
• W3091837215 hasConceptScore W3091837215C105795698 @default.
• W3091837215 hasConceptScore W3091837215C111030470 @default.
• W3091837215 hasConceptScore W3091837215C114614502 @default.
• W3091837215 hasConceptScore W3091837215C134306372 @default.
• W3091837215 hasConceptScore W3091837215C186450821 @default.
• W3091837215 hasConceptScore W3091837215C192939610 @default.
• W3091837215 hasConceptScore W3091837215C202444582 @default.
• W3091837215 hasConceptScore W3091837215C2524010 @default.
• W3091837215 hasConceptScore W3091837215C33923547 @default.
• W3091837215 hasConceptScore W3091837215C70943382 @default.
• W3091837215 hasLocation W30918372151 @default.
• W3091837215 hasOpenAccess W3091837215 @default.
• W3091837215 hasPrimaryLocation W30918372151 @default.
• W3091837215 hasRelatedWork W12400027 @default.
• W3091837215 hasRelatedWork W1585901754 @default.
• W3091837215 hasRelatedWork W1837237031 @default.
• W3091837215 hasRelatedWork W1982178893 @default.
• W3091837215 hasRelatedWork W1992790570 @default.
• W3091837215 hasRelatedWork W1995740892 @default.
• W3091837215 hasRelatedWork W2012919118 @default.
• W3091837215 hasRelatedWork W2027729304 @default.
• W3091837215 hasRelatedWork W2032624597 @default.
• W3091837215 hasRelatedWork W2058317090 @default.
• W3091837215 hasRelatedWork W2072931016 @default.
• W3091837215 hasRelatedWork W2197454702 @default.
• W3091837215 hasRelatedWork W2217701558 @default.
• W3091837215 hasRelatedWork W2887217883 @default.
• W3091837215 hasRelatedWork W2963261057 @default.
• W3091837215 hasRelatedWork W2978510797 @default.
• W3091837215 hasRelatedWork W2982355266 @default.
• W3091837215 hasRelatedWork W3021977414 @default.
• W3091837215 hasRelatedWork W3136276319 @default.
• W3091837215 hasRelatedWork W938876130 @default.
• W3091837215 isParatext "false" @default.

• next