A robust Hotelling test View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-04

AUTHORS

G. Willems, G. Pison, P. J. Rousseeuw, S. Van Aelst

ABSTRACT

Hotelling's T2 statistic is an important tool for inference about the center of a multivariate normal population. However, hypothesis tests and confidence intervals based on this statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator [9] instead of the classical mean and covariance matrix. Recently, a fast algorithm was constructed to compute the MCD [10]. In our test statistic we use the reweighted MCD, which has a higher efficiency. The distribution of this new statistic differs from the classical one. Therefore, the key problem is to find a good approximation for this distribution. Similarly to the classical T2 distribution, we obtain a multiple of a certain F-distribution. A Monte Carlo study shows that this distribution is an accurate approximation of the true distribution. Finally, the power and the robustness of the one-sample test based on our robust T2 are investigated through simulation. More... »

PAGES

125-138

Journal

TITLE

Metrika

ISSUE

1

VOLUME

55

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s001840200192

DOI

http://dx.doi.org/10.1007/s001840200192

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040082186


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/2008/0906", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Electrical and Electronic Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Antwerp", 
          "id": "https://www.grid.ac/institutes/grid.5284.b", 
          "name": [
            "Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Willems", 
        "givenName": "G.", 
        "id": "sg:person.012153775517.40", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012153775517.40"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Antwerp", 
          "id": "https://www.grid.ac/institutes/grid.5284.b", 
          "name": [
            "Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Pison", 
        "givenName": "G.", 
        "id": "sg:person.016576336236.11", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016576336236.11"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Antwerp", 
          "id": "https://www.grid.ac/institutes/grid.5284.b", 
          "name": [
            "Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rousseeuw", 
        "givenName": "P. J.", 
        "id": "sg:person.0775337371.63", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0775337371.63"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Antwerp", 
          "id": "https://www.grid.ac/institutes/grid.5284.b", 
          "name": [
            "Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Van Aelst", 
        "givenName": "S.", 
        "id": "sg:person.012217314753.64", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012217314753.64"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1080/00401706.1999.10485670", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058287776"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1984.10477105", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058302950"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1990.10474920", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058303860"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aos/1176349264", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064408821"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2531616", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069977056"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2002-04", 
    "datePublishedReg": "2002-04-01", 
    "description": "Hotelling's T2 statistic is an important tool for inference about the center of a multivariate normal population. However, hypothesis tests and confidence intervals based on this statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator [9] instead of the classical mean and covariance matrix. Recently, a fast algorithm was constructed to compute the MCD [10]. In our test statistic we use the reweighted MCD, which has a higher efficiency. The distribution of this new statistic differs from the classical one. Therefore, the key problem is to find a good approximation for this distribution. Similarly to the classical T2 distribution, we obtain a multiple of a certain F-distribution. A Monte Carlo study shows that this distribution is an accurate approximation of the true distribution. Finally, the power and the robustness of the one-sample test based on our robust T2 are investigated through simulation.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s001840200192", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1041634", 
        "issn": [
          "0026-1335", 
          "1435-926X"
        ], 
        "name": "Metrika", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "55"
      }
    ], 
    "name": "A robust Hotelling test", 
    "pagination": "125-138", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "beefd175abdc93e3853c127981b1bc7c3b49095cf62b4e7587fd608d6f378f54"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s001840200192"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1040082186"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s001840200192", 
      "https://app.dimensions.ai/details/publication/pub.1040082186"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T13:05", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8659_00000482.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/s001840200192"
  }
]
 

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/s001840200192'

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/s001840200192'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s001840200192'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s001840200192'


 

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

97 TRIPLES      21 PREDICATES      32 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s001840200192 schema:about anzsrc-for:09
2 anzsrc-for:0906
3 schema:author N1fc7bfc984ba49b9aa9dbab93822461a
4 schema:citation https://doi.org/10.1080/00401706.1999.10485670
5 https://doi.org/10.1080/01621459.1984.10477105
6 https://doi.org/10.1080/01621459.1990.10474920
7 https://doi.org/10.1214/aos/1176349264
8 https://doi.org/10.2307/2531616
9 schema:datePublished 2002-04
10 schema:datePublishedReg 2002-04-01
11 schema:description Hotelling's T2 statistic is an important tool for inference about the center of a multivariate normal population. However, hypothesis tests and confidence intervals based on this statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator [9] instead of the classical mean and covariance matrix. Recently, a fast algorithm was constructed to compute the MCD [10]. In our test statistic we use the reweighted MCD, which has a higher efficiency. The distribution of this new statistic differs from the classical one. Therefore, the key problem is to find a good approximation for this distribution. Similarly to the classical T2 distribution, we obtain a multiple of a certain F-distribution. A Monte Carlo study shows that this distribution is an accurate approximation of the true distribution. Finally, the power and the robustness of the one-sample test based on our robust T2 are investigated through simulation.
12 schema:genre research_article
13 schema:inLanguage en
14 schema:isAccessibleForFree false
15 schema:isPartOf N24e6008e01c544af843752fecdc7f7c1
16 Na64108d79e8549098641b67c9e6930d5
17 sg:journal.1041634
18 schema:name A robust Hotelling test
19 schema:pagination 125-138
20 schema:productId N1c8b7e710616465f8aa4b74a54494ad1
21 N80282d4fb5f541aaaa2e1c74bd9cbd9e
22 Ne1efe315fd4b45508c0a690c24d744bb
23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040082186
24 https://doi.org/10.1007/s001840200192
25 schema:sdDatePublished 2019-04-10T13:05
26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
27 schema:sdPublisher N33f3af7d08e54170b75f1105d943076a
28 schema:url http://link.springer.com/10.1007/s001840200192
29 sgo:license sg:explorer/license/
30 sgo:sdDataset articles
31 rdf:type schema:ScholarlyArticle
32 N1c8b7e710616465f8aa4b74a54494ad1 schema:name readcube_id
33 schema:value beefd175abdc93e3853c127981b1bc7c3b49095cf62b4e7587fd608d6f378f54
34 rdf:type schema:PropertyValue
35 N1fc7bfc984ba49b9aa9dbab93822461a rdf:first sg:person.012153775517.40
36 rdf:rest Nadafb4912fb143a99fb0a5ecd30450ea
37 N24e6008e01c544af843752fecdc7f7c1 schema:issueNumber 1
38 rdf:type schema:PublicationIssue
39 N33f3af7d08e54170b75f1105d943076a schema:name Springer Nature - SN SciGraph project
40 rdf:type schema:Organization
41 N80282d4fb5f541aaaa2e1c74bd9cbd9e schema:name dimensions_id
42 schema:value pub.1040082186
43 rdf:type schema:PropertyValue
44 Na64108d79e8549098641b67c9e6930d5 schema:volumeNumber 55
45 rdf:type schema:PublicationVolume
46 Nadafb4912fb143a99fb0a5ecd30450ea rdf:first sg:person.016576336236.11
47 rdf:rest Nafb276a7021f41d18e2d11658a4da905
48 Nafb276a7021f41d18e2d11658a4da905 rdf:first sg:person.0775337371.63
49 rdf:rest Nc23cb4dd9f4946a0b50d8ac935ec2e28
50 Nc23cb4dd9f4946a0b50d8ac935ec2e28 rdf:first sg:person.012217314753.64
51 rdf:rest rdf:nil
52 Ne1efe315fd4b45508c0a690c24d744bb schema:name doi
53 schema:value 10.1007/s001840200192
54 rdf:type schema:PropertyValue
55 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
56 schema:name Engineering
57 rdf:type schema:DefinedTerm
58 anzsrc-for:0906 schema:inDefinedTermSet anzsrc-for:
59 schema:name Electrical and Electronic Engineering
60 rdf:type schema:DefinedTerm
61 sg:journal.1041634 schema:issn 0026-1335
62 1435-926X
63 schema:name Metrika
64 rdf:type schema:Periodical
65 sg:person.012153775517.40 schema:affiliation https://www.grid.ac/institutes/grid.5284.b
66 schema:familyName Willems
67 schema:givenName G.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012153775517.40
69 rdf:type schema:Person
70 sg:person.012217314753.64 schema:affiliation https://www.grid.ac/institutes/grid.5284.b
71 schema:familyName Van Aelst
72 schema:givenName S.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012217314753.64
74 rdf:type schema:Person
75 sg:person.016576336236.11 schema:affiliation https://www.grid.ac/institutes/grid.5284.b
76 schema:familyName Pison
77 schema:givenName G.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016576336236.11
79 rdf:type schema:Person
80 sg:person.0775337371.63 schema:affiliation https://www.grid.ac/institutes/grid.5284.b
81 schema:familyName Rousseeuw
82 schema:givenName P. J.
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0775337371.63
84 rdf:type schema:Person
85 https://doi.org/10.1080/00401706.1999.10485670 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058287776
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1080/01621459.1984.10477105 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058302950
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1080/01621459.1990.10474920 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058303860
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1214/aos/1176349264 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064408821
92 rdf:type schema:CreativeWork
93 https://doi.org/10.2307/2531616 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069977056
94 rdf:type schema:CreativeWork
95 https://www.grid.ac/institutes/grid.5284.b schema:alternateName University of Antwerp
96 schema:name Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE
97 rdf:type schema:Organization
 




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


...