×

zbMATH — the first resource for mathematics

Sparsistent and constansistent estimation of the varying-coefficient model with a diverging number of predictors. (English) Zbl 1396.62083
Summary: The varying-coefficient model is a flexible class of approaches that extends simple linear relationships between covariates and responses. Two related problems concerning these models are selecting relevant variables and determining non-varying coefficients among those relevant ones. In this paper we study the sparsistency and constansistency of the regularized estimation approach when the number of predictors diverges with the sample size. Here, constansistency refers to the desired property that the non-zero, non-varying coefficients are identified with probability tending to one.
Reviewer: Reviewer (Berlin)
MSC:
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1080/00401706.1995.10484371 · doi:10.1080/00401706.1995.10484371
[2] DOI: 10.1080/01621459.1998.10473755 · doi:10.1080/01621459.1998.10473755
[3] DOI: 10.1198/016214501753168280 · Zbl 1018.62034 · doi:10.1198/016214501753168280
[4] Cho H., Statistica Sinica 23 pp 901– (2013)
[5] De Boor C., A Practical Guide to Splines (2001)
[6] DOI: 10.1111/j.1467-9868.2004.B5595.x · Zbl 1046.62033 · doi:10.1111/j.1467-9868.2004.B5595.x
[7] DOI: 10.3150/bj/1137421639 · Zbl 1098.62077 · doi:10.3150/bj/1137421639
[8] DOI: 10.1198/016214501753382273 · Zbl 1073.62547 · doi:10.1198/016214501753382273
[9] DOI: 10.1214/009053604000000256 · Zbl 1092.62031 · doi:10.1214/009053604000000256
[10] DOI: 10.1111/1467-9868.00233 · Zbl 04558573 · doi:10.1111/1467-9868.00233
[11] DOI: 10.4310/SII.2008.v1.n1.a15 · Zbl 1230.62031 · doi:10.4310/SII.2008.v1.n1.a15
[12] DOI: 10.1214/aos/1017939139 · Zbl 0977.62039 · doi:10.1214/aos/1017939139
[13] DOI: 10.1007/978-1-4757-3683-0 · doi:10.1007/978-1-4757-3683-0
[14] DOI: 10.1214/009053605000000110 · Zbl 1072.62027 · doi:10.1214/009053605000000110
[15] Hastie T., J. Roy. Statist. Soc. Ser. B-Methodol. 55 (4) pp 757– (1993)
[16] DOI: 10.1093/biomet/85.4.809 · Zbl 0921.62045 · doi:10.1093/biomet/85.4.809
[17] Hu T., Statistica Sinica 22 (2) pp 575– (2012)
[18] DOI: 10.1093/biomet/89.1.111 · Zbl 0998.62024 · doi:10.1093/biomet/89.1.111
[19] Huang J.H.Z., Statistica Sinica 14 (3) pp 763– (2004)
[20] DOI: 10.1214/009053605000000200 · Zbl 1078.62028 · doi:10.1214/009053605000000200
[21] DOI: 10.1111/biom.12020 · Zbl 1273.62254 · doi:10.1111/biom.12020
[22] DOI: 10.1198/016214508000001066 · Zbl 1286.62062 · doi:10.1198/016214508000001066
[23] Kwon S., Statist. Interface 6 pp 231– (2012)
[24] DOI: 10.1214/09-AOS720 · Zbl 1191.62101 · doi:10.1214/09-AOS720
[25] Li G., Statistica Sinica 21 (1) pp 391– (2011)
[26] DOI: 10.1016/j.jmva.2011.03.010 · Zbl 1216.62060 · doi:10.1016/j.jmva.2011.03.010
[27] DOI: 10.1214/009053607000000604 · Zbl 1132.62027 · doi:10.1214/009053607000000604
[28] DOI: 10.1080/07350015.2012.693851 · doi:10.1080/07350015.2012.693851
[29] DOI: 10.1214/009053606000000722 · Zbl 1106.62041 · doi:10.1214/009053606000000722
[30] DOI: 10.1214/12-EJS762 · Zbl 1295.62044 · doi:10.1214/12-EJS762
[31] DOI: 10.5705/ss.2010.121 · Zbl 1238.62021 · doi:10.5705/ss.2010.121
[32] Tibshirani R., J. Roy. Statist. Soc. Ser. B-Methodol. 58 (1) pp 267– (1996)
[33] DOI: 10.1111/j.1467-9868.2005.00490.x · Zbl 1060.62049 · doi:10.1111/j.1467-9868.2005.00490.x
[34] DOI: 10.1137/1.9781611970128 · doi:10.1137/1.9781611970128
[35] DOI: 10.1016/j.jmva.2012.05.006 · Zbl 1273.62093 · doi:10.1016/j.jmva.2012.05.006
[36] DOI: 10.1093/biomet/asm053 · Zbl 1135.62058 · doi:10.1093/biomet/asm053
[37] DOI: 10.1198/jasa.2009.0138 · Zbl 1388.62213 · doi:10.1198/jasa.2009.0138
[38] DOI: 10.1198/jasa.2009.tm09055 · Zbl 1205.62092 · doi:10.1198/jasa.2009.tm09055
[39] DOI: 10.1198/016214508000000788 · Zbl 1286.62034 · doi:10.1198/016214508000000788
[40] DOI: 10.1080/01621459.1998.10473800 · doi:10.1080/01621459.1998.10473800
[41] DOI: 10.1214/07-AOS580 · Zbl 1162.62037 · doi:10.1214/07-AOS580
[42] DOI: 10.1111/j.1467-9868.2005.00532.x · Zbl 1141.62030 · doi:10.1111/j.1467-9868.2005.00532.x
[43] DOI: 10.1111/j.1467-9868.2007.00581.x · Zbl 1120.62052 · doi:10.1111/j.1467-9868.2007.00581.x
[44] DOI: 10.1214/09-AOS729 · Zbl 1183.62120 · doi:10.1214/09-AOS729
[45] Zhang H.H., Statistica Sinica 16 (2) pp 659– (2006)
[46] DOI: 10.1198/jasa.2011.tm10281 · Zbl 1229.62051 · doi:10.1198/jasa.2011.tm10281
[47] DOI: 10.1016/j.spl.2009.07.004 · Zbl 1171.62026 · doi:10.1016/j.spl.2009.07.004
[48] DOI: 10.1198/016214506000000735 · Zbl 1171.62326 · doi:10.1198/016214506000000735
[49] DOI: 10.1214/009053607000000802 · Zbl 1142.62027 · doi:10.1214/009053607000000802
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.