Direct Estimation of Low-Dimensional Components in Additive Models
Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possib...
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| Veröffentlicht in: | The Annals of statistics 1998-06, Vol.26 (3), p.943-971 |
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| container_end_page | 971 |
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| container_issue | 3 |
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| container_title | The Annals of statistics |
| container_volume | 26 |
| creator | Fan, Jianqing Hardle, Wolfgang Mammen, Enno |
| description | Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this procedure is introduced. We consider weighted marginal integration for local linear fits and we show that this estimate has the following advantages. (i) With an appropriate choice of the weight function, the additive components can be efficiently estimated: An additive component can be estimated with the same asymptotic bias and variance as if the other components were known. (ii) Application of local linear fits reduces the design related bias. |
| doi_str_mv | 10.1214/aos/1024691083 |
| format | Article |
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Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this procedure is introduced. We consider weighted marginal integration for local linear fits and we show that this estimate has the following advantages. (i) With an appropriate choice of the weight function, the additive components can be efficiently estimated: An additive component can be estimated with the same asymptotic bias and variance as if the other components were known. (ii) Application of local linear fits reduces the design related bias.</description><subject>Approximation</subject><subject>Consistent estimators</subject><subject>Data smoothing</subject><subject>Density estimation</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Inference from stochastic processes; time series analysis</subject><subject>Linear inference, regression</subject><subject>Linear models</subject><subject>Linear regression</subject><subject>Mathematics</subject><subject>Multivariate analysis</subject><subject>Nonparametric Function Estimation</subject><subject>Probability and statistics</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Weighting functions</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><recordid>eNplkL1PwzAUxC0EEqWwsrBkYE37_BE33ihp-ZCCWOgcOc6L5CqNKzuA-O8xatQOTE863d376Qi5pTCjjIq5dmFOgQmpKOT8jEwYlXmaKynPyQRAQZpxKS7JVQhbAMiU4BPyuLIezZCsw2B3erCuT1yblO47Xdkd9iEKuksKt9u7HvshJLZPlk1jB_uFyZtrsAvX5KLVXcCb8U7J5mn9Ubyk5fvza7EsUyOEGlIlkNVYU2E0Qk5ZbiKSgVYBahRC5rDgdR2hskwjZ4bySNs0WrKaaY6ST8nDoXfv3TYy46fpbFPtfQT3P5XTtio25aiOJ25SnTaJFbNDhfEuBI_tMU2h-hvxf-B-_KmD0V3rdW9sOKYYX6gsz6Lt7mDbhsH5UykDkJz_ApZ4e2E</recordid><startdate>19980601</startdate><enddate>19980601</enddate><creator>Fan, Jianqing</creator><creator>Hardle, Wolfgang</creator><creator>Mammen, Enno</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19980601</creationdate><title>Direct Estimation of Low-Dimensional Components in Additive Models</title><author>Fan, Jianqing ; Hardle, Wolfgang ; Mammen, Enno</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c449t-94e2beb14cae08128c090c0f90eae4468073bb94355ae32c13364dda62b2a3e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Approximation</topic><topic>Consistent estimators</topic><topic>Data smoothing</topic><topic>Density estimation</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Inference from stochastic processes; time series analysis</topic><topic>Linear inference, regression</topic><topic>Linear models</topic><topic>Linear regression</topic><topic>Mathematics</topic><topic>Multivariate analysis</topic><topic>Nonparametric Function Estimation</topic><topic>Probability and statistics</topic><topic>Regression analysis</topic><topic>Sciences and techniques of general use</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Weighting functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fan, Jianqing</creatorcontrib><creatorcontrib>Hardle, Wolfgang</creatorcontrib><creatorcontrib>Mammen, Enno</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fan, Jianqing</au><au>Hardle, Wolfgang</au><au>Mammen, Enno</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Direct Estimation of Low-Dimensional Components in Additive Models</atitle><jtitle>The Annals of statistics</jtitle><date>1998-06-01</date><risdate>1998</risdate><volume>26</volume><issue>3</issue><spage>943</spage><epage>971</epage><pages>943-971</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | Approximation Consistent estimators Data smoothing Density estimation Estimators Exact sciences and technology Inference from stochastic processes time series analysis Linear inference, regression Linear models Linear regression Mathematics Multivariate analysis Nonparametric Function Estimation Probability and statistics Regression analysis Sciences and techniques of general use Statistical variance Statistics Weighting functions |
| title | Direct Estimation of Low-Dimensional Components in Additive Models |
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