Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data
Functional data analysis (FDA) has become an important area of statistics research in the recent decade, yet a smooth simultaneous confidence corridor (SCC) does not exist in the literature for the mean function of sparse functional data. SCC is a powerful tool for making statistical inference on an...
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| Veröffentlicht in: | Journal of the American Statistical Association 2014-06, Vol.109 (506), p.661-673 |
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| creator | Zheng, Shuzhuan Yang, Lijian Härdle, Wolfgang K. |
| description | Functional data analysis (FDA) has become an important area of statistics research in the recent decade, yet a smooth simultaneous confidence corridor (SCC) does not exist in the literature for the mean function of sparse functional data. SCC is a powerful tool for making statistical inference on an entire unknown function, nonetheless classic "Hungarian embedding" techniques for establishing asymptotic correctness of SCC completely fail for sparse functional data. We propose a local linear SCC and a shoal of confidence intervals (SCI) for the mean function of sparse functional data, and establish that it is asymptotically equivalent to the SCC of independent regression data, using new results from Gaussian process extreme value theory. The SCC procedure is examined in simulations for its superior theoretical accuracy and performance, and used to analyze growth curve data, confirming findings with quantified high significance levels. Supplementary materials for this article are available online. |
| doi_str_mv | 10.1080/01621459.2013.866899 |
| format | Article |
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SCC is a powerful tool for making statistical inference on an entire unknown function, nonetheless classic "Hungarian embedding" techniques for establishing asymptotic correctness of SCC completely fail for sparse functional data. We propose a local linear SCC and a shoal of confidence intervals (SCI) for the mean function of sparse functional data, and establish that it is asymptotically equivalent to the SCC of independent regression data, using new results from Gaussian process extreme value theory. The SCC procedure is examined in simulations for its superior theoretical accuracy and performance, and used to analyze growth curve data, confirming findings with quantified high significance levels. Supplementary materials for this article are available online.</description><subject>Analytical estimating</subject><subject>confidence interval</subject><subject>Confidence intervals</subject><subject>Data analysis</subject><subject>Data lines</subject><subject>Density estimation</subject><subject>Double sum</subject><subject>equations</subject><subject>Estimation methods</subject><subject>Estimation theory</subject><subject>Estimators</subject><subject>Extreme value</subject><subject>Inference</subject><subject>Karhunen-Loève L</subject><subject>Linear regression</subject><subject>Local linear estimator</subject><subject>Regression analysis</subject><subject>representation</subject><subject>Simulation</subject><subject>Statistical estimation</subject><subject>Statistical inference</subject><subject>Statistics</subject><subject>Strong approximation</subject><subject>Theory and Methods</subject><subject>Time series models</subject><issn>1537-274X</issn><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkVtLxDAQhYsouK7-A8WCz7tmmjRJn0TWK3h5WAXfwpgmbpdusyYp4r83S1V8cyDMwJxzEr5k2SGQKRBJTgnwAlhZTQsCdCo5l1W1lY2gpGJSCPay_WfezfZCWJJUQspR9jBfORcX-bxZ9W3Ezrg-5DPX2aY2nTZp9L6pnc9tOnFh8nuDXe5sPl-jDya_6jsdG9dhm19gxP1sx2IbzMF3H2fPV5dPs5vJ3eP17ez8bqIZsDh5pQJ0_UqQaWrBcoLG2NIAaARRalrxinBSUElrKUUtBaWMGVFrWkKNWNFxdjLkrr17702Iaul6n14RFHBJCiIKoEnFBpX2LgRvrFr7ZoX-UwFRG3Lqh5zakFMDuWQ7GmzLEJ3_9RSsYAIqlvZnw77pEpUVfjjf1iriZ-u89djpJij6zw3HQ4JFp_DNJ8PzPAl4-hZZcpD0Cy_9hu4</recordid><startdate>20140601</startdate><enddate>20140601</enddate><creator>Zheng, Shuzhuan</creator><creator>Yang, Lijian</creator><creator>Härdle, Wolfgang K.</creator><general>Taylor & Francis</general><general>Taylor & Francis Group, LLC</general><general>Taylor & Francis Ltd</general><scope>FBQ</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>K9.</scope></search><sort><creationdate>20140601</creationdate><title>Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data</title><author>Zheng, Shuzhuan ; Yang, Lijian ; Härdle, Wolfgang K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c414t-b371cdb0a4c3f1f60aeef5e11ca175c39690602383d887d873344e7dc351daa93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Analytical estimating</topic><topic>confidence interval</topic><topic>Confidence intervals</topic><topic>Data analysis</topic><topic>Data lines</topic><topic>Density estimation</topic><topic>Double sum</topic><topic>equations</topic><topic>Estimation methods</topic><topic>Estimation theory</topic><topic>Estimators</topic><topic>Extreme value</topic><topic>Inference</topic><topic>Karhunen-Loève L</topic><topic>Linear regression</topic><topic>Local linear estimator</topic><topic>Regression analysis</topic><topic>representation</topic><topic>Simulation</topic><topic>Statistical estimation</topic><topic>Statistical inference</topic><topic>Statistics</topic><topic>Strong approximation</topic><topic>Theory and Methods</topic><topic>Time series models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zheng, Shuzhuan</creatorcontrib><creatorcontrib>Yang, Lijian</creatorcontrib><creatorcontrib>Härdle, Wolfgang K.</creatorcontrib><collection>AGRIS</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Journal of the American Statistical Association</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zheng, Shuzhuan</au><au>Yang, Lijian</au><au>Härdle, Wolfgang K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>2014-06-01</date><risdate>2014</risdate><volume>109</volume><issue>506</issue><spage>661</spage><epage>673</epage><pages>661-673</pages><issn>1537-274X</issn><issn>0162-1459</issn><eissn>1537-274X</eissn><coden>JSTNAL</coden><abstract>Functional data analysis (FDA) has become an important area of statistics research in the recent decade, yet a smooth simultaneous confidence corridor (SCC) does not exist in the literature for the mean function of sparse functional data. SCC is a powerful tool for making statistical inference on an entire unknown function, nonetheless classic "Hungarian embedding" techniques for establishing asymptotic correctness of SCC completely fail for sparse functional data. We propose a local linear SCC and a shoal of confidence intervals (SCI) for the mean function of sparse functional data, and establish that it is asymptotically equivalent to the SCC of independent regression data, using new results from Gaussian process extreme value theory. The SCC procedure is examined in simulations for its superior theoretical accuracy and performance, and used to analyze growth curve data, confirming findings with quantified high significance levels. Supplementary materials for this article are available online.</abstract><cop>Alexandria</cop><pub>Taylor & Francis</pub><doi>10.1080/01621459.2013.866899</doi><tpages>13</tpages></addata></record> |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; Taylor & Francis Journals Complete |
| subjects | Analytical estimating confidence interval Confidence intervals Data analysis Data lines Density estimation Double sum equations Estimation methods Estimation theory Estimators Extreme value Inference Karhunen-Loève L Linear regression Local linear estimator Regression analysis representation Simulation Statistical estimation Statistical inference Statistics Strong approximation Theory and Methods Time series models |
| title | Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data |
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