Inference about the slope in linear regression: an empirical likelihood approach
We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also...
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| Veröffentlicht in: | Annals of the Institute of Statistical Mathematics 2019-02, Vol.71 (1), p.181-211 |
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| container_title | Annals of the Institute of Statistical Mathematics |
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| creator | Müller, Ursula U. Peng, Hanxiang Schick, Anton |
| description | We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719,
2017
), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study. |
| doi_str_mv | 10.1007/s10463-017-0632-y |
| format | Article |
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2017
), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study.</description><identifier>ISSN: 0020-3157</identifier><identifier>EISSN: 1572-9052</identifier><identifier>DOI: 10.1007/s10463-017-0632-y</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Computer simulation ; Confidence intervals ; Economic models ; Economics ; Empirical analysis ; Estimating techniques ; Finance ; Generalized method of moments ; Influence functions ; Insurance ; Likelihood ratio ; Management ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Regression analysis ; Statistical analysis ; Statistics ; Statistics for Business</subject><ispartof>Annals of the Institute of Statistical Mathematics, 2019-02, Vol.71 (1), p.181-211</ispartof><rights>The Institute of Statistical Mathematics, Tokyo 2017</rights><rights>Annals of the Institute of Statistical Mathematics is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-8ed4aaabad361a6a4a8188b7acfcb4d1650d19bdaeba5438a3bc0e364688e3b33</citedby><cites>FETCH-LOGICAL-c359t-8ed4aaabad361a6a4a8188b7acfcb4d1650d19bdaeba5438a3bc0e364688e3b33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10463-017-0632-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10463-017-0632-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Müller, Ursula U.</creatorcontrib><creatorcontrib>Peng, Hanxiang</creatorcontrib><creatorcontrib>Schick, Anton</creatorcontrib><title>Inference about the slope in linear regression: an empirical likelihood approach</title><title>Annals of the Institute of Statistical Mathematics</title><addtitle>Ann Inst Stat Math</addtitle><description>We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719,
2017
), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study.</description><subject>Computer simulation</subject><subject>Confidence intervals</subject><subject>Economic models</subject><subject>Economics</subject><subject>Empirical analysis</subject><subject>Estimating techniques</subject><subject>Finance</subject><subject>Generalized method of moments</subject><subject>Influence functions</subject><subject>Insurance</subject><subject>Likelihood ratio</subject><subject>Management</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Regression analysis</subject><subject>Statistical analysis</subject><subject>Statistics</subject><subject>Statistics for Business</subject><issn>0020-3157</issn><issn>1572-9052</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kLtOwzAUhi0EEqXwAGyWmA3HcS4uG6q4SZVggNk6dk7alNQOdjr07UkVBhamI_3nv0gfY9cSbiVAdZck5KUSICsBpcrE4YTNZFFlYgFFdspmABkINSrn7CKlLQCoTGUz9v7qG4rkHXG0YT_wYUM8daEn3nretZ4w8kjrSCm1wd9z9Jx2fRtbh934_6Ku3YRQc-z7GNBtLtlZg12iq987Z59Pjx_LF7F6e35dPqyEU8ViEJrqHBEt1qqUWGKOWmptK3SNs3ktywJqubA1ksUiVxqVdUCqzEutSVml5uxm6h1nv_eUBrMN--jHSSMXFegqV7IaXXJyuRhSitSYPrY7jAcjwRzBmQmcGcGZIzhzGDPZlEmj168p_mn-N_QDKK9yTA</recordid><startdate>20190201</startdate><enddate>20190201</enddate><creator>Müller, Ursula U.</creator><creator>Peng, Hanxiang</creator><creator>Schick, Anton</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20190201</creationdate><title>Inference about the slope in linear regression: an empirical likelihood approach</title><author>Müller, Ursula U. ; Peng, Hanxiang ; Schick, Anton</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-8ed4aaabad361a6a4a8188b7acfcb4d1650d19bdaeba5438a3bc0e364688e3b33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computer simulation</topic><topic>Confidence intervals</topic><topic>Economic models</topic><topic>Economics</topic><topic>Empirical analysis</topic><topic>Estimating techniques</topic><topic>Finance</topic><topic>Generalized method of moments</topic><topic>Influence functions</topic><topic>Insurance</topic><topic>Likelihood ratio</topic><topic>Management</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Regression analysis</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Statistics for Business</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Müller, Ursula U.</creatorcontrib><creatorcontrib>Peng, Hanxiang</creatorcontrib><creatorcontrib>Schick, Anton</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Annals of the Institute of Statistical Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Müller, Ursula U.</au><au>Peng, Hanxiang</au><au>Schick, Anton</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inference about the slope in linear regression: an empirical likelihood approach</atitle><jtitle>Annals of the Institute of Statistical Mathematics</jtitle><stitle>Ann Inst Stat Math</stitle><date>2019-02-01</date><risdate>2019</risdate><volume>71</volume><issue>1</issue><spage>181</spage><epage>211</epage><pages>181-211</pages><issn>0020-3157</issn><eissn>1572-9052</eissn><abstract>We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719,
2017
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| subjects | Computer simulation Confidence intervals Economic models Economics Empirical analysis Estimating techniques Finance Generalized method of moments Influence functions Insurance Likelihood ratio Management Mathematical models Mathematics Mathematics and Statistics Regression analysis Statistical analysis Statistics Statistics for Business |
| title | Inference about the slope in linear regression: an empirical likelihood approach |
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