Estimation of a Likelihood Ratio Ordered Family of Distributions
Statistics and Computing 34, 2024 Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption that $Q_x$ is isotonic in $x...
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| creator | Mösching, Alexandre Duembgen, Lutz |
| description | Statistics and Computing 34, 2024 Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in
\mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of
$Y$, given that $X = x$. The goal is to estimate these distributions under the
sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio
order. If the observations are identically distributed, a related goal is to
estimate the joint distribution $\mathcal{L}(X,Y)$ under the sole assumption
that it is totally positive of order two in a certain sense. An algorithm is
developed which estimates the unknown family of distributions $(Q_x)_x$ via
empirical likelihood. The benefit of the stronger regularization imposed by
likelihood ratio order over the usual stochastic order is evaluated in terms of
estimation and predictive performances on simulated as well as real data. |
| doi_str_mv | 10.48550/arxiv.2007.11521 |
| format | Article |
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\mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of
$Y$, given that $X = x$. The goal is to estimate these distributions under the
sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio
order. If the observations are identically distributed, a related goal is to
estimate the joint distribution $\mathcal{L}(X,Y)$ under the sole assumption
that it is totally positive of order two in a certain sense. An algorithm is
developed which estimates the unknown family of distributions $(Q_x)_x$ via
empirical likelihood. The benefit of the stronger regularization imposed by
likelihood ratio order over the usual stochastic order is evaluated in terms of
estimation and predictive performances on simulated as well as real data.</description><identifier>DOI: 10.48550/arxiv.2007.11521</identifier><language>eng</language><subject>Mathematics - Statistics Theory ; Statistics - Computation ; Statistics - Methodology ; Statistics - Theory</subject><creationdate>2020-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2007.11521$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.1007/s11222-023-10370-9$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2007.11521$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Mösching, Alexandre</creatorcontrib><creatorcontrib>Duembgen, Lutz</creatorcontrib><title>Estimation of a Likelihood Ratio Ordered Family of Distributions</title><description>Statistics and Computing 34, 2024 Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in
\mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of
$Y$, given that $X = x$. The goal is to estimate these distributions under the
sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio
order. If the observations are identically distributed, a related goal is to
estimate the joint distribution $\mathcal{L}(X,Y)$ under the sole assumption
that it is totally positive of order two in a certain sense. An algorithm is
developed which estimates the unknown family of distributions $(Q_x)_x$ via
empirical likelihood. The benefit of the stronger regularization imposed by
likelihood ratio order over the usual stochastic order is evaluated in terms of
estimation and predictive performances on simulated as well as real data.</description><subject>Mathematics - Statistics Theory</subject><subject>Statistics - Computation</subject><subject>Statistics - Methodology</subject><subject>Statistics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj01rwkAYhPfiQbQ_wFP3DyTuu0n241axaoWAIN7Du190aTSySUv99zXW08AwM8xDyAJYXqqqYktMv_En54zJHKDiMCVvm36IZxxid6FdoEjr-OXb-Nl1jh5Hmx6S88k7usVzbG9j6D32Q4rmeyz1czIJ2Pb-5akzctpuTuuPrD7s9utVnaGQkBkN2qJgXhqnywIN9xZLCFhoWQkhgxU2KJRKalQMgCuwnpfci8CNdaKYkdf_2QdCc0330-nWjCjNA6X4A_9xQ9s</recordid><startdate>20200722</startdate><enddate>20200722</enddate><creator>Mösching, Alexandre</creator><creator>Duembgen, Lutz</creator><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20200722</creationdate><title>Estimation of a Likelihood Ratio Ordered Family of Distributions</title><author>Mösching, Alexandre ; Duembgen, Lutz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-b919ca60e7bd943ab2eca41fa3975667fc6cf8a7879a8011281ce242e6f2bcd63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics - Statistics Theory</topic><topic>Statistics - Computation</topic><topic>Statistics - Methodology</topic><topic>Statistics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Mösching, Alexandre</creatorcontrib><creatorcontrib>Duembgen, Lutz</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Mösching, Alexandre</au><au>Duembgen, Lutz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimation of a Likelihood Ratio Ordered Family of Distributions</atitle><date>2020-07-22</date><risdate>2020</risdate><abstract>Statistics and Computing 34, 2024 Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in
\mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of
$Y$, given that $X = x$. The goal is to estimate these distributions under the
sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio
order. If the observations are identically distributed, a related goal is to
estimate the joint distribution $\mathcal{L}(X,Y)$ under the sole assumption
that it is totally positive of order two in a certain sense. An algorithm is
developed which estimates the unknown family of distributions $(Q_x)_x$ via
empirical likelihood. The benefit of the stronger regularization imposed by
likelihood ratio order over the usual stochastic order is evaluated in terms of
estimation and predictive performances on simulated as well as real data.</abstract><doi>10.48550/arxiv.2007.11521</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Statistics Theory Statistics - Computation Statistics - Methodology Statistics - Theory |
| title | Estimation of a Likelihood Ratio Ordered Family of Distributions |
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