Prediction and estimation of random variables with infinite mean or variance
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and finite variance. The proposed predictor is a generalized arith...
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| creator | de la Pena, Victor Gzyl, Henryk Mayoral, Silvia Zou, Haolin Alemayehu, Demissie |
| description | In this paper we propose an optimal predictor of a random variable that has
either an infinite mean or an infinite variance. The method consists of
transforming the random variable such that the transformed variable has a
finite mean and finite variance. The proposed predictor is a generalized
arithmetic mean which is similar to the notion of certainty price in utility
theory. Typically, the transformation consists of a parametric family of
bijections, in which case the parameter might be chosen to minimize the
prediction error in the transformed coordinates. The statistical properties of
the estimator of the proposed predictor are studied, and confidence intervals
are provided. The performance of the procedure is illustrated using simulated
and real data. |
| doi_str_mv | 10.48550/arxiv.2303.14752 |
| format | Article |
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either an infinite mean or an infinite variance. The method consists of
transforming the random variable such that the transformed variable has a
finite mean and finite variance. The proposed predictor is a generalized
arithmetic mean which is similar to the notion of certainty price in utility
theory. Typically, the transformation consists of a parametric family of
bijections, in which case the parameter might be chosen to minimize the
prediction error in the transformed coordinates. The statistical properties of
the estimator of the proposed predictor are studied, and confidence intervals
are provided. The performance of the procedure is illustrated using simulated
and real data.</description><identifier>DOI: 10.48550/arxiv.2303.14752</identifier><language>eng</language><subject>Mathematics - Statistics Theory ; Statistics - Methodology ; Statistics - Theory</subject><creationdate>2023-03</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/2303.14752$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2303.14752$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>de la Pena, Victor</creatorcontrib><creatorcontrib>Gzyl, Henryk</creatorcontrib><creatorcontrib>Mayoral, Silvia</creatorcontrib><creatorcontrib>Zou, Haolin</creatorcontrib><creatorcontrib>Alemayehu, Demissie</creatorcontrib><title>Prediction and estimation of random variables with infinite mean or variance</title><description>In this paper we propose an optimal predictor of a random variable that has
either an infinite mean or an infinite variance. The method consists of
transforming the random variable such that the transformed variable has a
finite mean and finite variance. The proposed predictor is a generalized
arithmetic mean which is similar to the notion of certainty price in utility
theory. Typically, the transformation consists of a parametric family of
bijections, in which case the parameter might be chosen to minimize the
prediction error in the transformed coordinates. The statistical properties of
the estimator of the proposed predictor are studied, and confidence intervals
are provided. The performance of the procedure is illustrated using simulated
and real data.</description><subject>Mathematics - Statistics Theory</subject><subject>Statistics - Methodology</subject><subject>Statistics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj81qwzAQhHXJIaR9gJyqF7CrP8vysYSmLRgSSO5mZcl0IZaDbPLz9lWdnJbZGYb5CFlzlitTFOwd4g0vuZBM5lyVhViSeh-9w3bCIVAIjvpxwh5mOXQ0ptfQ0wtEBHvyI73i9EsxdBhw8rT3kGLx4YfWv5BFB6fRvz7vihy2n8fNd1bvvn42H3UGuhSZ09KoSgjgzClu2lIDWF1AJZVhLUgGYJwFa43nJTdJ6Mrq5CqVElyuyNujdaZpzjENjvfmn6qZqeQf0IhHqA</recordid><startdate>20230326</startdate><enddate>20230326</enddate><creator>de la Pena, Victor</creator><creator>Gzyl, Henryk</creator><creator>Mayoral, Silvia</creator><creator>Zou, Haolin</creator><creator>Alemayehu, Demissie</creator><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20230326</creationdate><title>Prediction and estimation of random variables with infinite mean or variance</title><author>de la Pena, Victor ; Gzyl, Henryk ; Mayoral, Silvia ; Zou, Haolin ; Alemayehu, Demissie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-d6384922a10d418c76aab65a93480ca30aa8dbabb8e1718a8d69b69344434813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Statistics Theory</topic><topic>Statistics - Methodology</topic><topic>Statistics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>de la Pena, Victor</creatorcontrib><creatorcontrib>Gzyl, Henryk</creatorcontrib><creatorcontrib>Mayoral, Silvia</creatorcontrib><creatorcontrib>Zou, Haolin</creatorcontrib><creatorcontrib>Alemayehu, Demissie</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>de la Pena, Victor</au><au>Gzyl, Henryk</au><au>Mayoral, Silvia</au><au>Zou, Haolin</au><au>Alemayehu, Demissie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Prediction and estimation of random variables with infinite mean or variance</atitle><date>2023-03-26</date><risdate>2023</risdate><abstract>In this paper we propose an optimal predictor of a random variable that has
either an infinite mean or an infinite variance. The method consists of
transforming the random variable such that the transformed variable has a
finite mean and finite variance. The proposed predictor is a generalized
arithmetic mean which is similar to the notion of certainty price in utility
theory. Typically, the transformation consists of a parametric family of
bijections, in which case the parameter might be chosen to minimize the
prediction error in the transformed coordinates. The statistical properties of
the estimator of the proposed predictor are studied, and confidence intervals
are provided. The performance of the procedure is illustrated using simulated
and real data.</abstract><doi>10.48550/arxiv.2303.14752</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Statistics Theory Statistics - Methodology Statistics - Theory |
| title | Prediction and estimation of random variables with infinite mean or variance |
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