Simultaneous confidence bands for nonparametric regression with missing covariate data
We consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the estimator and the true regression function is derived and an asymptotically accura...
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| Veröffentlicht in: | Annals of the Institute of Statistical Mathematics 2021-12, Vol.73 (6), p.1249-1279 |
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| container_end_page | 1279 |
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| container_issue | 6 |
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| container_title | Annals of the Institute of Statistical Mathematics |
| container_volume | 73 |
| creator | Cai, Li Gu, Lijie Wang, Qihua Wang, Suojin |
| description | We consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the estimator and the true regression function is derived and an asymptotically accurate simultaneous confidence band is constructed. The estimator for the regression function is shown to be oracally efficient in the sense that it is uniformly indistinguishable from that when the selection probabilities are known. Finite sample performance is examined via simulation studies which support our asymptotic theory. The proposed method is demonstrated via an analysis of a data set from the Canada 2010/2011 Youth Student Survey. |
| doi_str_mv | 10.1007/s10463-021-00784-5 |
| format | Article |
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The asymptotic distribution of the maximal deviation between the estimator and the true regression function is derived and an asymptotically accurate simultaneous confidence band is constructed. The estimator for the regression function is shown to be oracally efficient in the sense that it is uniformly indistinguishable from that when the selection probabilities are known. Finite sample performance is examined via simulation studies which support our asymptotic theory. The proposed method is demonstrated via an analysis of a data set from the Canada 2010/2011 Youth Student Survey.</description><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Economics</subject><subject>Finance</subject><subject>Insurance</subject><subject>Management</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonparametric statistics</subject><subject>Regression</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>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOI7-AVcB19GbpGmapQy-YMCFj21I27RmmCZj0ir-ezNWcCd3cTmXc86FD6FzCpcUQF4lCkXJCTBKsqwKIg7QggrJiALBDtECgAHh-XKMTlLaAABnnC3Q65Mbpu1ovA1Twk3wnWutbyyujW8T7kLEPvidiWawY3QNjraPNiUXPP504xseXBa-z9EPE50ZLW7NaE7RUWe2yZ797iV6ub15Xt2T9ePdw-p6TRpO1UikKGtRNrLgpRC2Vl1XGcVazpu6sHlKKKkQoEyhlBElrWlFQVFrlawpl5Iv0cXcu4vhfbJp1JswRZ9faiaqQhZKCJFdbHY1MaQUbad30Q0mfmkKes9Pz_x05qd_-Ol9iM-hlM2-t_Gv-p_UN7chcx4</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Cai, Li</creator><creator>Gu, Lijie</creator><creator>Wang, Qihua</creator><creator>Wang, Suojin</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>20211201</creationdate><title>Simultaneous confidence bands for nonparametric regression with missing covariate data</title><author>Cai, Li ; Gu, Lijie ; Wang, Qihua ; Wang, Suojin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-756b56c743655eb9ff8a92d33cb4e4e460615509a499a561b181091ee97b13773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic properties</topic><topic>Economics</topic><topic>Finance</topic><topic>Insurance</topic><topic>Management</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonparametric statistics</topic><topic>Regression</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Statistics for Business</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cai, Li</creatorcontrib><creatorcontrib>Gu, Lijie</creatorcontrib><creatorcontrib>Wang, Qihua</creatorcontrib><creatorcontrib>Wang, Suojin</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>Cai, Li</au><au>Gu, Lijie</au><au>Wang, Qihua</au><au>Wang, Suojin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simultaneous confidence bands for nonparametric regression with missing covariate data</atitle><jtitle>Annals of the Institute of Statistical Mathematics</jtitle><stitle>Ann Inst Stat Math</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>73</volume><issue>6</issue><spage>1249</spage><epage>1279</epage><pages>1249-1279</pages><issn>0020-3157</issn><eissn>1572-9052</eissn><abstract>We consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. 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| source | Springer Nature - Complete Springer Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Asymptotic methods Asymptotic properties Economics Finance Insurance Management Mathematics Mathematics and Statistics Nonparametric statistics Regression Statistical analysis Statistics Statistics for Business |
| title | Simultaneous confidence bands for nonparametric regression with missing covariate data |
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