Non-parametric small area estimation using penalized spline regression
The paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2008-02, Vol.70 (1), p.265-286 |
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| container_end_page | 286 |
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| container_title | Journal of the Royal Statistical Society. Series B, Statistical methodology |
| container_volume | 70 |
| creator | Opsomer, J. D. Claeskens, G. Ranalli, M. G. Kauermann, G. Breidt, F. J. |
| description | The paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean-squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non-parametric bootstrap approach for model inference and estimation of the small area prediction mean-squared error. The applicability of the method is demonstrated on a survey of lakes in north-eastern USA. |
| doi_str_mv | 10.1111/j.1467-9868.2007.00635.x |
| format | Article |
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D. ; Claeskens, G. ; Ranalli, M. G. ; Kauermann, G. ; Breidt, F. J.</creator><creatorcontrib>Opsomer, J. D. ; Claeskens, G. ; Ranalli, M. G. ; Kauermann, G. ; Breidt, F. J.</creatorcontrib><description>The paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean-squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non-parametric bootstrap approach for model inference and estimation of the small area prediction mean-squared error. The applicability of the method is demonstrated on a survey of lakes in north-eastern USA.</description><identifier>ISSN: 1369-7412</identifier><identifier>EISSN: 1467-9868</identifier><identifier>DOI: 10.1111/j.1467-9868.2007.00635.x</identifier><language>eng</language><publisher>Oxford, UK: Blackwell Publishing Ltd</publisher><subject>Approximation ; Approximations and expansions ; Best linear unbiased prediction ; Bootstrap inference ; Bootstrap mechanism ; Bootstrap method ; Estimation ; Estimation methods ; Estimators ; Exact sciences and technology ; General topics ; Geographical information systems ; Lakes ; Mathematical analysis ; Mathematics ; Maximum likelihood estimation ; Maximum likelihood method ; Mixed model ; Modeling ; Natural resource survey ; Natural resources ; Nonparametric models ; Numerical analysis ; Numerical analysis. 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D.</creatorcontrib><creatorcontrib>Claeskens, G.</creatorcontrib><creatorcontrib>Ranalli, M. G.</creatorcontrib><creatorcontrib>Kauermann, G.</creatorcontrib><creatorcontrib>Breidt, F. J.</creatorcontrib><title>Non-parametric small area estimation using penalized spline regression</title><title>Journal of the Royal Statistical Society. Series B, Statistical methodology</title><description>The paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean-squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non-parametric bootstrap approach for model inference and estimation of the small area prediction mean-squared error. The applicability of the method is demonstrated on a survey of lakes in north-eastern USA.</description><subject>Approximation</subject><subject>Approximations and expansions</subject><subject>Best linear unbiased prediction</subject><subject>Bootstrap inference</subject><subject>Bootstrap mechanism</subject><subject>Bootstrap method</subject><subject>Estimation</subject><subject>Estimation methods</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Geographical information systems</subject><subject>Lakes</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood method</subject><subject>Mixed model</subject><subject>Modeling</subject><subject>Natural resource survey</subject><subject>Natural resources</subject><subject>Nonparametric models</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical approximation</subject><subject>Parametric inference</subject><subject>Parametric models</subject><subject>Probability and statistics</subject><subject>Ratio test</subject><subject>Sciences and techniques of general use</subject><subject>Spatial analysis</subject><subject>Spatial models</subject><subject>Statistical methods</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Studies</subject><subject>U.S.A</subject><issn>1369-7412</issn><issn>1467-9868</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqNUl2L1TAQLaLguvoThCLoW2s-2iR98EEv7up1WWHXr7chTdM1Nf0w6dV7_fVO7XIRnxyYzJA5Zzg5JElSSnKK8bzLaSFkVimhckaIzAkRvMz3d5KT4-Au9lxUmSwou588iLEjGELyk-TschyySQfd2zk4k8Zee5_qYHVq4-x6PbtxSHfRDTfpZAft3S_bpHHybrBpsDfBxoiIh8m9VvtoH93W0-Tj2esPmzfZxfvzt5uXF5kRRVFmylqj2qKhwsqSqKaVmlAt26IWpW5QvdCF5IoYLQVrFGF1Y-pCWiEqYkTZ8NPk2bp3CuP3HSqE3kVjvdeDHXcRuFC8YhVH4JN_gN24C6g_ArpUlZWQFEFqBZkwxhhsC1PAJ4cDUAKLu9DBYiIsJi48CX_chT1Stys12MmaI6_2uhtDjDX8AK4lweOAiVSFxWFSzGm5EiUwJeDr3OOyp7didTTat0EPxsXjUmQzSsmi98WK--m8Pfy3WLi6vn6FHfIfr_wuzmP4az8jXDGG82yduzjb_XGuwzfAzyJL-Hx5Dtvtp5Jebd7BF_4bm3K_Mw</recordid><startdate>200802</startdate><enddate>200802</enddate><creator>Opsomer, J. 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| identifier | ISSN: 1369-7412 |
| ispartof | Journal of the Royal Statistical Society. Series B, Statistical methodology, 2008-02, Vol.70 (1), p.265-286 |
| issn | 1369-7412 1467-9868 |
| language | eng |
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| source | Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); RePEc; Wiley Online Library Journals Frontfile Complete; Business Source Complete; JSTOR Mathematics & Statistics |
| subjects | Approximation Approximations and expansions Best linear unbiased prediction Bootstrap inference Bootstrap mechanism Bootstrap method Estimation Estimation methods Estimators Exact sciences and technology General topics Geographical information systems Lakes Mathematical analysis Mathematics Maximum likelihood estimation Maximum likelihood method Mixed model Modeling Natural resource survey Natural resources Nonparametric models Numerical analysis Numerical analysis. Scientific computation Numerical approximation Parametric inference Parametric models Probability and statistics Ratio test Sciences and techniques of general use Spatial analysis Spatial models Statistical methods Statistical variance Statistics Studies U.S.A |
| title | Non-parametric small area estimation using penalized spline regression |
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