×

Tuning parameter selector for the penalized likelihood method in multivariate generalized linear models. (English) Zbl 1462.62448

Summary: Variable selection is fundamental to high-dimensional multivariate generalized linear models. The smoothly clipped absolute deviation (SCAD) method can solve the problem of variable selection and estimation. The choice of the tuning parameter in the SCAD method is critical, which controls the complexity of the selected model. This article proposes a criterion to select the tuning parameter for the SCAD method in multivariate generalized linear models, which is shown to be able to identify the true model consistently. Simulation studies are conducted to support theoretical findings, and two real data analysis are given to illustrate the proposed method.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62J12 Generalized linear models (logistic models)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akaike, 2nd International Symposium on Information Theory pp 267– (1973)
[2] DOI: 10.1214/aos/1176345976 · Zbl 0526.62026 · doi:10.1214/aos/1176345976
[3] DOI: 10.1016/S0378-3758(02)00284-7 · Zbl 1027.62015 · doi:10.1016/S0378-3758(02)00284-7
[4] DOI: 10.1007/978-1-4757-3454-6 · doi:10.1007/978-1-4757-3454-6
[5] DOI: 10.1198/016214501753382273 · Zbl 1073.62547 · doi:10.1198/016214501753382273
[6] James H. A., J. Amer. Statist. Assoc. 88 pp 669– (1993) · doi:10.1080/01621459.1993.10476321
[7] DOI: 10.1016/j.spl.2004.11.021 · Zbl 1065.62128 · doi:10.1016/j.spl.2004.11.021
[8] DOI: 10.1023/A:1007608224229 · Zbl 0969.68669 · doi:10.1023/A:1007608224229
[9] McCullagh P., Generalized Linear Models., 2. ed. (1989) · Zbl 0744.62098
[10] DOI: 10.1214/aos/1176344136 · Zbl 0379.62005 · doi:10.1214/aos/1176344136
[11] Sha N., Biometrics 60 (3) pp 812– (2004) · Zbl 1274.62428 · doi:10.1111/j.0006-341X.2004.00233.x
[12] Tibshirani R. J., J. Roy. Statist. Soc. Ser. B 58 pp 267– (1996)
[13] Wang H., J. Amer. Statist. Assoc. 101 pp 1418– (2007)
[14] DOI: 10.1093/biomet/asm053 · Zbl 1135.62058 · doi:10.1093/biomet/asm053
[15] DOI: 10.1198/jasa.2009.tm08013 · Zbl 1397.62262 · doi:10.1198/jasa.2009.tm08013
[16] DOI: 10.1198/016214506000000735 · Zbl 1171.62326 · doi:10.1198/016214506000000735
[17] 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.