Document Zbl 07643164

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Korean Stat. Soc.</a> <a href="/?q=in%3A491714" title="Articles in this Issue">51, No. 4, 1302-1325 (2022)</a>; correction ibid. 51, No. 4, 1326 (2022). </div> <div class="abstract">Summary: In this paper, a robust, efficient and easily implemented estimation procedure for single-index varying-coefficient models is proposed by combining minimum average variance estimation (MAVE) with exponential squared loss. The merit of the proposed method is robust against outliers or heavy-tailed error distributions while asymptotically efficient as the original MAVE under the normal error case. A practical minorization-maximization algorithm is proposed for implementation. Under some regularity conditions, asymptotic distributions of the resulting estimators are derived. Simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both theoretical and empirical findings confirm that our proposed method works very well.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7643164">Cited in <strong>1</strong> Review</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aasymptotic+properties">asymptotic properties</a>; <a href="/?q=ut%3Aexponential+squared+loss">exponential squared loss</a>; <a href="/?q=ut%3AMAVE">MAVE</a>; <a href="/?q=ut%3Arobustness">robustness</a>; <a href="/?q=ut%3Asingle-index+varying-coefficient+models">single-index varying-coefficient models</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07643164" data-ciurl="/ci/07643164" data-biburl="/bibtex/07643164.bib" data-amsurl="/amsrefs/07643164.bib" data-xmlurl="/xml/07643164.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07643164.pdf" title="Zbl 07643164 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s42952-022-00187-z" aria-label="DOI for “Robust MAVE for single-index varying-coefficient models”" title="10.1007/s42952-022-00187-z">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Fan, JQ; Yao, QW; Cai, ZW, Adaptive varying-coefficient linear models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 57-80 (2003) · <a href="/1063.62054" class="nowrap">Zbl 1063.62054</a> · <a href="https://doi.org/10.1111/1467-9868.00372" class="nowrap">doi:10.1111/1467-9868.00372</a></td> </tr><tr> <td>[2]</td> <td class="space">Fan, JQ; Zhang, WY, Statistical methods with varying coefficient models, Statistics and Its Interface, 1, 179-195 (2008) · <a href="/1230.62031" class="nowrap">Zbl 1230.62031</a> · <a href="https://doi.org/10.4310/SII.2008.v1.n1.a15" class="nowrap">doi:10.4310/SII.2008.v1.n1.a15</a></td> </tr><tr> <td>[3]</td> <td class="space">Feng, SY; Tian, P.; Hu, YP; Li, GR, Estimation in functional single-index varying coefficient model, Journal of Statistical Planning and Inference, 214, 62-75 (2021) · <a href="/1460.62050" class="nowrap">Zbl 1460.62050</a> · <a href="https://doi.org/10.1016/j.jspi.2021.01.003" class="nowrap">doi:10.1016/j.jspi.2021.01.003</a></td> </tr><tr> <td>[4]</td> <td class="space">Feng, SY; Xue, LG, Variable selection for single-index varying-coefficient model, Frontiers of Mathematics in China, 8, 541-565 (2013) · <a href="/1273.62121" class="nowrap">Zbl 1273.62121</a> · <a href="https://doi.org/10.1007/s11464-013-0284-z" class="nowrap">doi:10.1007/s11464-013-0284-z</a></td> </tr><tr> <td>[5]</td> <td class="space">Feng, SY; Xue, LG, Model detection and estimation for single-index varying coefficient model, Journal of Multivariate Analysis, 139, 227-244 (2015) · <a href="/1328.62205" class="nowrap">Zbl 1328.62205</a> · <a href="https://doi.org/10.1016/j.jmva.2015.03.008" class="nowrap">doi:10.1016/j.jmva.2015.03.008</a></td> </tr><tr> <td>[6]</td> <td class="space">Friedman, J.; Hastie, T.; Tibshirani, R., Additive logistic regression: A statistical view of boosting, The Annals of Statistics, 28, 337-407 (2000) · <a href="/1106.62323" class="nowrap">Zbl 1106.62323</a> · <a href="https://doi.org/10.1214/aos/1016218223" class="nowrap">doi:10.1214/aos/1016218223</a></td> </tr><tr> <td>[7]</td> <td class="space">Härdle, W.; Hall, P.; Ichimura, H., Optimal smoothing in single-index models, The Annals of Statistics, 21, 157-178 (1993) · <a href="/0770.62049" class="nowrap">Zbl 0770.62049</a> · <a href="https://doi.org/10.1214/aos/1176349020" class="nowrap">doi:10.1214/aos/1176349020</a></td> </tr><tr> <td>[8]</td> <td class="space">Harrison, D.; Rubinfeld, DL, Hedonic housing pries and the demand for clean air, Journal of Environmental Economics and Management, 5, 81-102 (1978) · <a href="/0375.90023" class="nowrap">Zbl 0375.90023</a> · <a href="https://doi.org/10.1016/0095-0696(78)90006-2" class="nowrap">doi:10.1016/0095-0696(78)90006-2</a></td> </tr><tr> <td>[9]</td> <td class="space">Hu, T.; Xia, YC, Adaptive semi-varying coefficient model selection, Statistica Sinica, 22, 575-599 (2012) · <a href="/1511.62168" class="nowrap">Zbl 1511.62168</a> · <a href="https://doi.org/10.5705/ss.2010.105" class="nowrap">doi:10.5705/ss.2010.105</a></td> </tr><tr> <td>[10]</td> <td class="space">Huang, ZS; Pang, Z.; Lin, BQ; Shao, QX, Model structure selection in single-index-coefficient regression models, Journal of Multivariate Analysis, 125, 159-175 (2014) · <a href="/1280.62039" class="nowrap">Zbl 1280.62039</a> · <a href="https://doi.org/10.1016/j.jmva.2013.12.006" class="nowrap">doi:10.1016/j.jmva.2013.12.006</a></td> </tr><tr> <td>[11]</td> <td class="space">Jiang, YL, Robust estimation in partially linear regression models, Journal of Applied Statistics, 42, 2497-2508 (2015) · <a href="/1514.62646" class="nowrap">Zbl 1514.62646</a> · <a href="https://doi.org/10.1080/02664763.2015.1043862" class="nowrap">doi:10.1080/02664763.2015.1043862</a></td> </tr><tr> <td>[12]</td> <td class="space">Jiang, YL; Ji, QH; Xie, BJ, Robust estimation for the varying coefficient partially nonlinear models, Journal of Computational and Applied Mathematics, 326, 31-43 (2017) · <a href="/1368.62137" class="nowrap">Zbl 1368.62137</a> · <a href="https://doi.org/10.1016/j.cam.2017.04.028" class="nowrap">doi:10.1016/j.cam.2017.04.028</a></td> </tr><tr> <td>[13]</td> <td class="space">Lai, P.; Zhang, QZ; Lian, H.; Wang, QH, Efficient estimation for the heteroscedastic single-index varying coefficient models, Statistics and Probability Letters, 110, 84-93 (2016) · <a href="/1383.62088" class="nowrap">Zbl 1383.62088</a> · <a href="https://doi.org/10.1016/j.spl.2015.12.005" class="nowrap">doi:10.1016/j.spl.2015.12.005</a></td> </tr><tr> <td>[14]</td> <td class="space">Li, GR; Peng, H.; Dong, K.; Tong, TJ, Simultaneous confidence bands and hypothesis testing in single-index models, Statistica Sinica, 24, 937-955 (2014) · <a href="/1285.62044" class="nowrap">Zbl 1285.62044</a></td> </tr><tr> <td>[15]</td> <td class="space">Lian, H.; Liang, H.; Carroll, RJ, Variance function partially linear single-index models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77, 171-194 (2015) · <a href="/1414.62301" class="nowrap">Zbl 1414.62301</a> · <a href="https://doi.org/10.1111/rssb.12066" class="nowrap">doi:10.1111/rssb.12066</a></td> </tr><tr> <td>[16]</td> <td class="space">Liu, JC; Xu, PR; Lian, H., Estimation for single-index models via martingale difference divergence, Computational Statistics and Data Analysis, 137, 271-284 (2019) · <a href="/1507.62112" class="nowrap">Zbl 1507.62112</a> · <a href="https://doi.org/10.1016/j.csda.2019.03.008" class="nowrap">doi:10.1016/j.csda.2019.03.008</a></td> </tr><tr> <td>[17]</td> <td class="space">Peng, H.; Huang, T., Penalized least squares for single index models, Journal of Statistical Planning and Inference, 141, 1362-1379 (2011) · <a href="/1204.62070" class="nowrap">Zbl 1204.62070</a> · <a href="https://doi.org/10.1016/j.jspi.2010.10.003" class="nowrap">doi:10.1016/j.jspi.2010.10.003</a></td> </tr><tr> <td>[18]</td> <td class="space">Powell, JL; Stock, JH; Stoker, TM, Semiparametric estimation of index coefficients, Econometrica, 57, 1403-1430 (1989) · <a href="/0683.62070" class="nowrap">Zbl 0683.62070</a> · <a href="https://doi.org/10.2307/1913713" class="nowrap">doi:10.2307/1913713</a></td> </tr><tr> <td>[19]</td> <td class="space">Shi, JH; Yang, Q.; Li, XY; Song, WX, Effects of measurement error on a class of single-index varying coefficient regression models, Computational Statistics, 32, 977-1001 (2017) · <a href="/1417.62094" class="nowrap">Zbl 1417.62094</a> · <a href="https://doi.org/10.1007/s00180-017-0726-2" class="nowrap">doi:10.1007/s00180-017-0726-2</a></td> </tr><tr> <td>[20]</td> <td class="space">Song, YQ; Jian, L.; Lin, L., Robust exponential squared loss-based variable selection for high-dimensional single-index varying-coefficient model, Journal of Computational and Applied Mathematics, 308, 330-345 (2016) · <a href="/1346.62083" class="nowrap">Zbl 1346.62083</a> · <a href="https://doi.org/10.1016/j.cam.2016.05.030" class="nowrap">doi:10.1016/j.cam.2016.05.030</a></td> </tr><tr> <td>[21]</td> <td class="space">Wang, JL; Xue, LG; Zhu, LX; Chong, YS, Estimation for a partial-linear single-index model, The Annals of Statistics, 38, 246-274 (2010) · <a href="/1181.62038" class="nowrap">Zbl 1181.62038</a> · <a href="https://doi.org/10.1214/09-AOS712" class="nowrap">doi:10.1214/09-AOS712</a></td> </tr><tr> <td>[22]</td> <td class="space">Wang, QH; Xue, LG, Statistical inference in partially-varying-coefficient single-index model, Journal of Multivariate Analysis, 102, 1-19 (2011) · <a href="/1206.62113" class="nowrap">Zbl 1206.62113</a> · <a href="https://doi.org/10.1016/j.jmva.2010.07.005" class="nowrap">doi:10.1016/j.jmva.2010.07.005</a></td> </tr><tr> <td>[23]</td> <td class="space">Wang, XQ; Jiang, YL; Huang, M.; Zhang, HP, Robust variable selection with exponential squared loss, Journal of the American Statistical Association, 108, 632-643 (2013) · <a href="/06195966" class="nowrap">Zbl 06195966</a> · <a href="https://doi.org/10.1080/01621459.2013.766613" class="nowrap">doi:10.1080/01621459.2013.766613</a></td> </tr><tr> <td>[24]</td> <td class="space">Xia, YC, Asymptotic distributions for two estimators of the single-index model, Econometric Theory, 22, 1112-1137 (2006) · <a href="/1170.62323" class="nowrap">Zbl 1170.62323</a> · <a href="https://doi.org/10.1017/S0266466606060531" class="nowrap">doi:10.1017/S0266466606060531</a></td> </tr><tr> <td>[25]</td> <td class="space">Xia, YC; Li, WK, On single-index coefficient regression models, Journal of the American Statistical Association, 94, 1275-1285 (1999) · <a href="/1069.62548" class="nowrap">Zbl 1069.62548</a> · <a href="https://doi.org/10.1080/01621459.1999.10473880" class="nowrap">doi:10.1080/01621459.1999.10473880</a></td> </tr><tr> <td>[26]</td> <td class="space">Xia, YC; Tong, H.; Li, WK; Zhu, LX, An adaptive estimation of dimension reduction space, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 363-410 (2002) · <a href="/1091.62028" class="nowrap">Zbl 1091.62028</a> · <a href="https://doi.org/10.1111/1467-9868.03411" class="nowrap">doi:10.1111/1467-9868.03411</a></td> </tr><tr> <td>[27]</td> <td class="space">Xue, LG; Pang, Z., Statistical inference for a single-index varying-coefficient model, Statistics and Computing, 23, 589-599 (2013) · <a href="/1322.62126" class="nowrap">Zbl 1322.62126</a> · <a href="https://doi.org/10.1007/s11222-012-9332-x" class="nowrap">doi:10.1007/s11222-012-9332-x</a></td> </tr><tr> <td>[28]</td> <td class="space">Yu, P.; Zhu, ZY; Zhang, ZZ, Robust exponential squared loss-based estimation in semi-functional linear regression models, Computational Statistics, 34, 503-525 (2019) · <a href="/1417.62103" class="nowrap">Zbl 1417.62103</a> · <a href="https://doi.org/10.1007/s00180-018-0810-2" class="nowrap">doi:10.1007/s00180-018-0810-2</a></td> </tr><tr> <td>[29]</td> <td class="space">Yue, LL; Li, GR; Lian, H., Identification and estimation in quantile varying-coefficient models with unknown link function, Test, 28, 4, 1251-1275 (2019) · <a href="/1439.62107" class="nowrap">Zbl 1439.62107</a> · <a href="https://doi.org/10.1007/s11749-019-00638-6" class="nowrap">doi:10.1007/s11749-019-00638-6</a></td> </tr><tr> <td>[30]</td> <td class="space">Zhang, WY; Li, DG; Xia, YC, Estimation in generalised varying-coefficient models with unspecified link functions, Journal of Econometrics, 187, 238-255 (2015) · <a href="/1337.62086" class="nowrap">Zbl 1337.62086</a> · <a href="https://doi.org/10.1016/j.jeconom.2015.02.022" class="nowrap">doi:10.1016/j.jeconom.2015.02.022</a></td> </tr><tr> <td>[31]</td> <td class="space">Zhang, WY; Zhang, H., Simultaneous confidence band and hypothesis test in generalised varying-coefficient models, Journal of Multivariate Analysis, 101, 1656-1680 (2010) · <a href="/1189.62085" class="nowrap">Zbl 1189.62085</a> · <a href="https://doi.org/10.1016/j.jmva.2010.03.003" class="nowrap">doi:10.1016/j.jmva.2010.03.003</a></td> </tr><tr> <td>[32]</td> <td class="space">Zhao, Y.; Xue, LG; Feng, SY, Semiparametric estimation of the single-index varying-coefficient model, Communications in Statistics-Theory and Methods, 46, 4311-4326 (2017) · <a href="/1422.62146" class="nowrap">Zbl 1422.62146</a> · <a href="https://doi.org/10.1080/03610926.2015.1081950" class="nowrap">doi:10.1080/03610926.2015.1081950</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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