On the exceedance point process for a stationary sequence View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1988-03

AUTHORS

T. Hsing, J. Hüsler, M. R. Leadbetter

ABSTRACT

It is known that the exceedance points of a high level by a stationary sequence are asymptotically Poisson as the level increases, under appropriate long range and local dependence conditions. When the local dependence conditions are relaxed, clustering of exceedances may occur, based on Poisson positions for the clusters. In this paper a detailed analysis of the exceedance point process is given, and shows that, under wide conditions, any limiting point process for exceedances is necessarily compound Poisson. More generally the possible random measure limits for normalized exceedance point processes are characterized. Sufficient conditions are also given for the existence of a point process limit. The limiting distributions of extreme order statistics are derived as corollaries. More... »

PAGES

97-112

References to SciGraph publications

  • 1974-12. On extreme values in stationary sequences in PROBABILITY THEORY AND RELATED FIELDS
  • 1976-03. Weak convergence of high level exceedances by a stationary sequence in PROBABILITY THEORY AND RELATED FIELDS
  • 1983-12. Extremes and local dependence in stationary sequences in PROBABILITY THEORY AND RELATED FIELDS
  • 1983. Extremes and Related Properties of Random Sequences and Processes in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00718038

    DOI

    http://dx.doi.org/10.1007/bf00718038

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1019718520


    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, Texas A&M University, 77843, College Station, TX", 
              "id": "http://www.grid.ac/institutes/grid.264756.4", 
              "name": [
                "Department of Statistics, Texas A&M University, 77843, College Station, TX"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hsing", 
            "givenName": "T.", 
            "id": "sg:person.01223332210.42", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01223332210.42"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Universit\u00e4t Bern, Bern, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.5734.5", 
              "name": [
                "Department of Mathematics, Universit\u00e4t Bern, Bern, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "H\u00fcsler", 
            "givenName": "J.", 
            "id": "sg:person.01003720107.94", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01003720107.94"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Statistics, University of North Carolina, 27154, Chapel Hill, NC", 
              "id": "http://www.grid.ac/institutes/grid.410711.2", 
              "name": [
                "Department of Statistics, University of North Carolina, 27154, Chapel Hill, NC"
              ], 
              "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"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-1-4612-5449-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018032998", 
              "https://doi.org/10.1007/978-1-4612-5449-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00532947", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006825626", 
              "https://doi.org/10.1007/bf00532947"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00532685", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014293467", 
              "https://doi.org/10.1007/bf00532685"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00532484", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023261655", 
              "https://doi.org/10.1007/bf00532484"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1988-03", 
        "datePublishedReg": "1988-03-01", 
        "description": "It is known that the exceedance points of a high level by a stationary sequence are asymptotically Poisson as the level increases, under appropriate long range and local dependence conditions. When the local dependence conditions are relaxed, clustering of exceedances may occur, based on Poisson positions for the clusters. In this paper a detailed analysis of the exceedance point process is given, and shows that, under wide conditions, any limiting point process for exceedances is necessarily compound Poisson. More generally the possible random measure limits for normalized exceedance point processes are characterized. Sufficient conditions are also given for the existence of a point process limit. The limiting distributions of extreme order statistics are derived as corollaries.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf00718038", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1053886", 
            "issn": [
              "0178-8051", 
              "1432-2064"
            ], 
            "name": "Probability Theory and Related Fields", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "78"
          }
        ], 
        "keywords": [
          "exceedance point processes", 
          "point process", 
          "stationary sequence", 
          "dependence conditions", 
          "extreme order statistics", 
          "point process limit", 
          "order statistics", 
          "compound Poisson", 
          "sufficient conditions", 
          "Poisson", 
          "wide conditions", 
          "statistics", 
          "corollary", 
          "exceedance", 
          "existence", 
          "conditions", 
          "process limits", 
          "detailed analysis", 
          "limit", 
          "point", 
          "long range", 
          "process", 
          "sequence", 
          "distribution", 
          "clusters", 
          "analysis", 
          "range", 
          "position", 
          "level increases", 
          "levels", 
          "high levels", 
          "increase", 
          "paper", 
          "exceedance points", 
          "appropriate long range", 
          "local dependence conditions", 
          "Poisson positions", 
          "possible random measure limits", 
          "random measure limits", 
          "measure limits", 
          "normalized exceedance point processes"
        ], 
        "name": "On the exceedance point process for a stationary sequence", 
        "pagination": "97-112", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1019718520"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00718038"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00718038", 
          "https://app.dimensions.ai/details/publication/pub.1019718520"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:04", 
        "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/article/article_202.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf00718038"
      }
    ]
     

    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/bf00718038'

    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/bf00718038'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00718038'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00718038'


     

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

    135 TRIPLES      22 PREDICATES      71 URIs      59 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00718038 schema:about anzsrc-for:01
    2 anzsrc-for:0104
    3 schema:author Ned3a3063167345b897017e837b286568
    4 schema:citation sg:pub.10.1007/978-1-4612-5449-2
    5 sg:pub.10.1007/bf00532484
    6 sg:pub.10.1007/bf00532685
    7 sg:pub.10.1007/bf00532947
    8 schema:datePublished 1988-03
    9 schema:datePublishedReg 1988-03-01
    10 schema:description It is known that the exceedance points of a high level by a stationary sequence are asymptotically Poisson as the level increases, under appropriate long range and local dependence conditions. When the local dependence conditions are relaxed, clustering of exceedances may occur, based on Poisson positions for the clusters. In this paper a detailed analysis of the exceedance point process is given, and shows that, under wide conditions, any limiting point process for exceedances is necessarily compound Poisson. More generally the possible random measure limits for normalized exceedance point processes are characterized. Sufficient conditions are also given for the existence of a point process limit. The limiting distributions of extreme order statistics are derived as corollaries.
    11 schema:genre article
    12 schema:inLanguage en
    13 schema:isAccessibleForFree true
    14 schema:isPartOf N11fddbcbf02543518f600c57142cbf34
    15 Nb2223e80139c460e9b205f36e204a683
    16 sg:journal.1053886
    17 schema:keywords Poisson
    18 Poisson positions
    19 analysis
    20 appropriate long range
    21 clusters
    22 compound Poisson
    23 conditions
    24 corollary
    25 dependence conditions
    26 detailed analysis
    27 distribution
    28 exceedance
    29 exceedance point processes
    30 exceedance points
    31 existence
    32 extreme order statistics
    33 high levels
    34 increase
    35 level increases
    36 levels
    37 limit
    38 local dependence conditions
    39 long range
    40 measure limits
    41 normalized exceedance point processes
    42 order statistics
    43 paper
    44 point
    45 point process
    46 point process limit
    47 position
    48 possible random measure limits
    49 process
    50 process limits
    51 random measure limits
    52 range
    53 sequence
    54 stationary sequence
    55 statistics
    56 sufficient conditions
    57 wide conditions
    58 schema:name On the exceedance point process for a stationary sequence
    59 schema:pagination 97-112
    60 schema:productId N479109bf59704e368aad4de3cf2118ad
    61 Nf9ab668c6aad4c87a7eda8b0e40ee4ed
    62 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019718520
    63 https://doi.org/10.1007/bf00718038
    64 schema:sdDatePublished 2022-01-01T18:04
    65 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    66 schema:sdPublisher Nab99023dc8904b26ae7dcfbf96eef956
    67 schema:url https://doi.org/10.1007/bf00718038
    68 sgo:license sg:explorer/license/
    69 sgo:sdDataset articles
    70 rdf:type schema:ScholarlyArticle
    71 N11fddbcbf02543518f600c57142cbf34 schema:volumeNumber 78
    72 rdf:type schema:PublicationVolume
    73 N3c02ff1cd0764f1fa59cdcd89d005780 rdf:first sg:person.01003720107.94
    74 rdf:rest Nb5f3e3f348394acb90df357807c0068f
    75 N479109bf59704e368aad4de3cf2118ad schema:name dimensions_id
    76 schema:value pub.1019718520
    77 rdf:type schema:PropertyValue
    78 Nab99023dc8904b26ae7dcfbf96eef956 schema:name Springer Nature - SN SciGraph project
    79 rdf:type schema:Organization
    80 Nb2223e80139c460e9b205f36e204a683 schema:issueNumber 1
    81 rdf:type schema:PublicationIssue
    82 Nb5f3e3f348394acb90df357807c0068f rdf:first sg:person.010453124705.04
    83 rdf:rest rdf:nil
    84 Ned3a3063167345b897017e837b286568 rdf:first sg:person.01223332210.42
    85 rdf:rest N3c02ff1cd0764f1fa59cdcd89d005780
    86 Nf9ab668c6aad4c87a7eda8b0e40ee4ed schema:name doi
    87 schema:value 10.1007/bf00718038
    88 rdf:type schema:PropertyValue
    89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    90 schema:name Mathematical Sciences
    91 rdf:type schema:DefinedTerm
    92 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
    93 schema:name Statistics
    94 rdf:type schema:DefinedTerm
    95 sg:journal.1053886 schema:issn 0178-8051
    96 1432-2064
    97 schema:name Probability Theory and Related Fields
    98 schema:publisher Springer Nature
    99 rdf:type schema:Periodical
    100 sg:person.01003720107.94 schema:affiliation grid-institutes:grid.5734.5
    101 schema:familyName Hüsler
    102 schema:givenName J.
    103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01003720107.94
    104 rdf:type schema:Person
    105 sg:person.010453124705.04 schema:affiliation grid-institutes:grid.410711.2
    106 schema:familyName Leadbetter
    107 schema:givenName M. R.
    108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010453124705.04
    109 rdf:type schema:Person
    110 sg:person.01223332210.42 schema:affiliation grid-institutes:grid.264756.4
    111 schema:familyName Hsing
    112 schema:givenName T.
    113 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01223332210.42
    114 rdf:type schema:Person
    115 sg:pub.10.1007/978-1-4612-5449-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018032998
    116 https://doi.org/10.1007/978-1-4612-5449-2
    117 rdf:type schema:CreativeWork
    118 sg:pub.10.1007/bf00532484 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023261655
    119 https://doi.org/10.1007/bf00532484
    120 rdf:type schema:CreativeWork
    121 sg:pub.10.1007/bf00532685 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014293467
    122 https://doi.org/10.1007/bf00532685
    123 rdf:type schema:CreativeWork
    124 sg:pub.10.1007/bf00532947 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006825626
    125 https://doi.org/10.1007/bf00532947
    126 rdf:type schema:CreativeWork
    127 grid-institutes:grid.264756.4 schema:alternateName Department of Statistics, Texas A&M University, 77843, College Station, TX
    128 schema:name Department of Statistics, Texas A&M University, 77843, College Station, TX
    129 rdf:type schema:Organization
    130 grid-institutes:grid.410711.2 schema:alternateName Department of Statistics, University of North Carolina, 27154, Chapel Hill, NC
    131 schema:name Department of Statistics, University of North Carolina, 27154, Chapel Hill, NC
    132 rdf:type schema:Organization
    133 grid-institutes:grid.5734.5 schema:alternateName Department of Mathematics, Universität Bern, Bern, Switzerland
    134 schema:name Department of Mathematics, Universität Bern, Bern, Switzerland
    135 rdf:type schema:Organization
     




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


    ...