On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1989

AUTHORS

M. R. Leadbetter , S. Nandagopalan

ABSTRACT

It is known ([1]) that any point process limit for the (time normalized) exceedances of high levels by a stationary sequence is necessarily Compound Poisson, under general dependence restrictions. This results from the clustering of exceedances where the underlying Poisson points represent cluster positions, and the multiplicities correspond to cluster sizes.Here we investigate a class of stationary sequences satisfying a mild local dependence condition restricting the extent of local “rapid oscillation”. For this class, criteria are given for the existence and value of the so-called “extremal index” which plays a key role in determining the intensity of cluster positions. Cluster size distributions are investigated for this class and in particular shown to be asymptotically equivalent to those for lengths of runs of consecutive exceedances above the level. Relations between the point processes of exceedances, cluster centers, and upcrossings are discussed. More... »

PAGES

69-80

Book

TITLE

Extreme Value Theory

ISBN

978-0-387-96954-1
978-1-4612-3634-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4612-3634-4_7

DOI

http://dx.doi.org/10.1007/978-1-4612-3634-4_7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021546814


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA", 
          "id": "http://www.grid.ac/institutes/grid.410711.2", 
          "name": [
            "Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Leadbetter", 
        "givenName": "M. R.", 
        "id": "sg:person.010453124705.04", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010453124705.04"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA", 
          "id": "http://www.grid.ac/institutes/grid.410711.2", 
          "name": [
            "Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Nandagopalan", 
        "givenName": "S.", 
        "id": "sg:person.013600411571.68", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013600411571.68"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1989", 
    "datePublishedReg": "1989-01-01", 
    "description": "It is known ([1]) that any point process limit for the (time normalized) exceedances of high levels by a stationary sequence is necessarily Compound Poisson, under general dependence restrictions. This results from the clustering of exceedances where the underlying Poisson points represent cluster positions, and the multiplicities correspond to cluster sizes.Here we investigate a class of stationary sequences satisfying a mild local dependence condition restricting the extent of local \u201crapid oscillation\u201d. For this class, criteria are given for the existence and value of the so-called \u201cextremal index\u201d which plays a key role in determining the intensity of cluster positions. Cluster size distributions are investigated for this class and in particular shown to be asymptotically equivalent to those for lengths of runs of consecutive exceedances above the level. Relations between the point processes of exceedances, cluster centers, and upcrossings are discussed.", 
    "editor": [
      {
        "familyName": "H\u00fcsler", 
        "givenName": "J\u00fcrg", 
        "type": "Person"
      }, 
      {
        "familyName": "Reiss", 
        "givenName": "Rolf-Dieter", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4612-3634-4_7", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-0-387-96954-1", 
        "978-1-4612-3634-4"
      ], 
      "name": "Extreme Value Theory", 
      "type": "Book"
    }, 
    "keywords": [
      "stationary sequence", 
      "clustering of exceedances", 
      "point process", 
      "point process limit", 
      "compound Poisson", 
      "dependence restrictions", 
      "Poisson points", 
      "class", 
      "dependence conditions", 
      "extremal index", 
      "cluster size distribution", 
      "length of run", 
      "consecutive exceedances", 
      "cluster centers", 
      "exceedance point processes", 
      "process limits", 
      "exceedance", 
      "Poisson", 
      "restriction", 
      "clustering", 
      "cluster positions", 
      "multiplicity", 
      "rapid oscillations", 
      "oscillations", 
      "existence", 
      "upcrossings", 
      "limit", 
      "sequence", 
      "point", 
      "position", 
      "size", 
      "conditions", 
      "criteria", 
      "values", 
      "index", 
      "size distribution", 
      "distribution", 
      "length", 
      "run", 
      "relation", 
      "process", 
      "high levels", 
      "levels", 
      "extent", 
      "key role", 
      "role", 
      "intensity", 
      "center", 
      "general dependence restrictions", 
      "underlying Poisson points", 
      "mild local dependence condition", 
      "local dependence conditions", 
      "Mild Oscillation Restrictions", 
      "Oscillation Restrictions"
    ], 
    "name": "On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions", 
    "pagination": "69-80", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1021546814"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4612-3634-4_7"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4612-3634-4_7", 
      "https://app.dimensions.ai/details/publication/pub.1021546814"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-01-01T19:28", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/chapter/chapter_94.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-1-4612-3634-4_7"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-3634-4_7'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-3634-4_7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-3634-4_7'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-3634-4_7'


 

This table displays all metadata directly associated to this object as RDF triples.

126 TRIPLES      23 PREDICATES      80 URIs      73 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4612-3634-4_7 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Nc145176ca274404dbf4e80b33042f66e
4 schema:datePublished 1989
5 schema:datePublishedReg 1989-01-01
6 schema:description It is known ([1]) that any point process limit for the (time normalized) exceedances of high levels by a stationary sequence is necessarily Compound Poisson, under general dependence restrictions. This results from the clustering of exceedances where the underlying Poisson points represent cluster positions, and the multiplicities correspond to cluster sizes.Here we investigate a class of stationary sequences satisfying a mild local dependence condition restricting the extent of local “rapid oscillation”. For this class, criteria are given for the existence and value of the so-called “extremal index” which plays a key role in determining the intensity of cluster positions. Cluster size distributions are investigated for this class and in particular shown to be asymptotically equivalent to those for lengths of runs of consecutive exceedances above the level. Relations between the point processes of exceedances, cluster centers, and upcrossings are discussed.
7 schema:editor N4ae8f574c1534226b069732833aa5d20
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N675d805121d348578a9c86cc3cfb1626
12 schema:keywords Mild Oscillation Restrictions
13 Oscillation Restrictions
14 Poisson
15 Poisson points
16 center
17 class
18 cluster centers
19 cluster positions
20 cluster size distribution
21 clustering
22 clustering of exceedances
23 compound Poisson
24 conditions
25 consecutive exceedances
26 criteria
27 dependence conditions
28 dependence restrictions
29 distribution
30 exceedance
31 exceedance point processes
32 existence
33 extent
34 extremal index
35 general dependence restrictions
36 high levels
37 index
38 intensity
39 key role
40 length
41 length of run
42 levels
43 limit
44 local dependence conditions
45 mild local dependence condition
46 multiplicity
47 oscillations
48 point
49 point process
50 point process limit
51 position
52 process
53 process limits
54 rapid oscillations
55 relation
56 restriction
57 role
58 run
59 sequence
60 size
61 size distribution
62 stationary sequence
63 underlying Poisson points
64 upcrossings
65 values
66 schema:name On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions
67 schema:pagination 69-80
68 schema:productId N54af0c03348f4e11aa15502c598bdfc8
69 Ne18e7d2c4e8f456ea34ac69127e2304d
70 schema:publisher N8cda899c5d7f4dadb0231f3b1ea7c08f
71 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021546814
72 https://doi.org/10.1007/978-1-4612-3634-4_7
73 schema:sdDatePublished 2022-01-01T19:28
74 schema:sdLicense https://scigraph.springernature.com/explorer/license/
75 schema:sdPublisher N7c0fce5fcc97414eaa9f7000212315be
76 schema:url https://doi.org/10.1007/978-1-4612-3634-4_7
77 sgo:license sg:explorer/license/
78 sgo:sdDataset chapters
79 rdf:type schema:Chapter
80 N28b6bf320ccb422eb8ca23215b45a9d4 rdf:first Na19213eebade406d8437ca2e89d95c26
81 rdf:rest rdf:nil
82 N45ab230413954c28869bc217daf84654 rdf:first sg:person.013600411571.68
83 rdf:rest rdf:nil
84 N4ae8f574c1534226b069732833aa5d20 rdf:first Nfda8928b391c43be97b2c673c88000ca
85 rdf:rest N28b6bf320ccb422eb8ca23215b45a9d4
86 N54af0c03348f4e11aa15502c598bdfc8 schema:name doi
87 schema:value 10.1007/978-1-4612-3634-4_7
88 rdf:type schema:PropertyValue
89 N675d805121d348578a9c86cc3cfb1626 schema:isbn 978-0-387-96954-1
90 978-1-4612-3634-4
91 schema:name Extreme Value Theory
92 rdf:type schema:Book
93 N7c0fce5fcc97414eaa9f7000212315be schema:name Springer Nature - SN SciGraph project
94 rdf:type schema:Organization
95 N8cda899c5d7f4dadb0231f3b1ea7c08f schema:name Springer Nature
96 rdf:type schema:Organisation
97 Na19213eebade406d8437ca2e89d95c26 schema:familyName Reiss
98 schema:givenName Rolf-Dieter
99 rdf:type schema:Person
100 Nc145176ca274404dbf4e80b33042f66e rdf:first sg:person.010453124705.04
101 rdf:rest N45ab230413954c28869bc217daf84654
102 Ne18e7d2c4e8f456ea34ac69127e2304d schema:name dimensions_id
103 schema:value pub.1021546814
104 rdf:type schema:PropertyValue
105 Nfda8928b391c43be97b2c673c88000ca schema:familyName Hüsler
106 schema:givenName Jürg
107 rdf:type schema:Person
108 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
109 schema:name Mathematical Sciences
110 rdf:type schema:DefinedTerm
111 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
112 schema:name Statistics
113 rdf:type schema:DefinedTerm
114 sg:person.010453124705.04 schema:affiliation grid-institutes:grid.410711.2
115 schema:familyName Leadbetter
116 schema:givenName M. R.
117 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010453124705.04
118 rdf:type schema:Person
119 sg:person.013600411571.68 schema:affiliation grid-institutes:grid.410711.2
120 schema:familyName Nandagopalan
121 schema:givenName S.
122 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013600411571.68
123 rdf:type schema:Person
124 grid-institutes:grid.410711.2 schema:alternateName Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA
125 schema:name Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA
126 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...