L1 Properties of the Nadaraya Quantile Estimator
Let X be a real random variable having f as density function. Let F be its cumulative distribution function and Q its quantile function. For h > 0, let F h and Q h denote respectively the Nadaraya kernel estimator of F and Q . In the first part of this paper the almost sure convergence of the con...
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| Veröffentlicht in: | Sankhya A 2022-08, Vol.84 (2), p.867-884 |
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| container_title | Sankhya A |
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| creator | Youndjé, É. |
| description | Let
X
be a real random variable having
f
as density function. Let
F
be its cumulative distribution function and
Q
its quantile function. For
h
> 0, let
F
h
and
Q
h
denote respectively the Nadaraya kernel estimator of
F
and
Q
. In the first part of this paper the almost sure convergence of the conventional
L
1
distance between
Q
h
and
Q
is established. In the second part, the
L
1
right inversion
distance is introduced. The representation of this
L
1
right inversion distance in terms of
F
h
and
F
is given. This representation allows us to suggest ways to choose a
global
bandwidth for the estimator
Q
h
. |
| doi_str_mv | 10.1007/s13171-020-00225-0 |
| format | Article |
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X
be a real random variable having
f
as density function. Let
F
be its cumulative distribution function and
Q
its quantile function. For
h
> 0, let
F
h
and
Q
h
denote respectively the Nadaraya kernel estimator of
F
and
Q
. In the first part of this paper the almost sure convergence of the conventional
L
1
distance between
Q
h
and
Q
is established. In the second part, the
L
1
right inversion
distance is introduced. The representation of this
L
1
right inversion distance in terms of
F
h
and
F
is given. This representation allows us to suggest ways to choose a
global
bandwidth for the estimator
Q
h
.</description><identifier>ISSN: 0976-836X</identifier><identifier>ISSN: 0972-7671</identifier><identifier>EISSN: 0976-8378</identifier><identifier>EISSN: 0976-836X</identifier><identifier>DOI: 10.1007/s13171-020-00225-0</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Humanities and Social Sciences ; Mathematics and Statistics ; Methods and statistics ; Statistical Theory and Methods ; Statistics ; Statistics and Computing/Statistics Programs</subject><ispartof>Sankhya A, 2022-08, Vol.84 (2), p.867-884</ispartof><rights>Indian Statistical Institute 2020</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1730-7d580988c3233fea13a8516b68f2249a54ddb624b6f9450da9f4c5984a5d406e3</citedby><cites>FETCH-LOGICAL-c1730-7d580988c3233fea13a8516b68f2249a54ddb624b6f9450da9f4c5984a5d406e3</cites><orcidid>0000-0001-8546-4530</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13171-020-00225-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13171-020-00225-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27903,27904,41467,42536,51297</link.rule.ids><backlink>$$Uhttps://shs.hal.science/halshs-04645168$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Youndjé, É.</creatorcontrib><title>L1 Properties of the Nadaraya Quantile Estimator</title><title>Sankhya A</title><addtitle>Sankhya A</addtitle><description>Let
X
be a real random variable having
f
as density function. Let
F
be its cumulative distribution function and
Q
its quantile function. For
h
> 0, let
F
h
and
Q
h
denote respectively the Nadaraya kernel estimator of
F
and
Q
. In the first part of this paper the almost sure convergence of the conventional
L
1
distance between
Q
h
and
Q
is established. In the second part, the
L
1
right inversion
distance is introduced. The representation of this
L
1
right inversion distance in terms of
F
h
and
F
is given. This representation allows us to suggest ways to choose a
global
bandwidth for the estimator
Q
h
.</description><subject>Humanities and Social Sciences</subject><subject>Mathematics and Statistics</subject><subject>Methods and statistics</subject><subject>Statistical Theory and Methods</subject><subject>Statistics</subject><subject>Statistics and Computing/Statistics Programs</subject><issn>0976-836X</issn><issn>0972-7671</issn><issn>0976-8378</issn><issn>0976-836X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kNtKAzEQhoMoWGpfwKt9AKOTc_aylGoLiwdQ8C5MdxO7pXZLshX69kZXeuncZAj_9w98hFwzuGUA5i4xwQyjwIECcK4onJERlEZTK4w9P-36_ZJMUtpAHlFyI_iIQMWK59jtfexbn4ouFP3aF4_YYMQjFi8H3PXt1hfz1Lef2HfxilwE3CY_-XvH5O1-_jpb0OrpYTmbVrRmRgA1jbJQWlsLLkTwyARaxfRK28C5LFHJpllpLlc6lFJBg2WQtSqtRNVI0F6Myc3Qu8at28d8PB5dh61bTCuX_9I6OZBa5lL7xXKcD_E6dilFH04MA_djyQ2WXLbkfi05yJAYoJTDuw8f3aY7xF0u_4_6BopGZ4I</recordid><startdate>202208</startdate><enddate>202208</enddate><creator>Youndjé, É.</creator><general>Springer India</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>BXJBU</scope><orcidid>https://orcid.org/0000-0001-8546-4530</orcidid></search><sort><creationdate>202208</creationdate><title>L1 Properties of the Nadaraya Quantile Estimator</title><author>Youndjé, É.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1730-7d580988c3233fea13a8516b68f2249a54ddb624b6f9450da9f4c5984a5d406e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Humanities and Social Sciences</topic><topic>Mathematics and Statistics</topic><topic>Methods and statistics</topic><topic>Statistical Theory and Methods</topic><topic>Statistics</topic><topic>Statistics and Computing/Statistics Programs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Youndjé, É.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>HAL-SHS: Archive ouverte en Sciences de l'Homme et de la Société</collection><jtitle>Sankhya A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Youndjé, É.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>L1 Properties of the Nadaraya Quantile Estimator</atitle><jtitle>Sankhya A</jtitle><stitle>Sankhya A</stitle><date>2022-08</date><risdate>2022</risdate><volume>84</volume><issue>2</issue><spage>867</spage><epage>884</epage><pages>867-884</pages><issn>0976-836X</issn><issn>0972-7671</issn><eissn>0976-8378</eissn><eissn>0976-836X</eissn><abstract>Let
X
be a real random variable having
f
as density function. Let
F
be its cumulative distribution function and
Q
its quantile function. For
h
> 0, let
F
h
and
Q
h
denote respectively the Nadaraya kernel estimator of
F
and
Q
. In the first part of this paper the almost sure convergence of the conventional
L
1
distance between
Q
h
and
Q
is established. In the second part, the
L
1
right inversion
distance is introduced. The representation of this
L
1
right inversion distance in terms of
F
h
and
F
is given. This representation allows us to suggest ways to choose a
global
bandwidth for the estimator
Q
h
.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s13171-020-00225-0</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0001-8546-4530</orcidid></addata></record> |
| fulltext | fulltext |
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| issn | 0976-836X 0972-7671 0976-8378 0976-836X |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Humanities and Social Sciences Mathematics and Statistics Methods and statistics Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs |
| title | L1 Properties of the Nadaraya Quantile Estimator |
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