zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Variable selection for semiparametric varying coefficient partially linear models. (English) Zbl 1171.62026
Summary: We present a variable selection procedure by combining basis function approximations with SCAD penalty for semiparametric varying coefficient partially linear models. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
MSC:
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
65C05Monte Carlo methods
References:
[1]Fan, J. Q.; Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties, J. amer. Statist. assoc. 96, 1348-1360 (2001) · Zbl 1073.62547 · doi:10.1198/016214501753382273
[2]Fan, J.; Li, R.: New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis, J. amer. Statist. assoc. 99, 710-723 (2004) · Zbl 1117.62329 · doi:10.1198/016214504000001060 · doi:http://masetto.asa.catchword.org/vl=1887686/cl=20/nw=1/rpsv/cw/asa/01621459/v99n467/s20/p710
[3]Fan, J. Q.; Huang, T.: Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli 11, 1031-1057 (2005) · Zbl 1098.62077 · doi:10.3150/bj/1137421639 · doi:euclid:bj/1137421639
[4]Frank, I. E.; Friedman, J. H.: A statistical view of some chemometrics regression tools, Technometrics 35, 109-148 (1993) · Zbl 0775.62288 · doi:10.2307/1269656
[5]He, X. M.; Zhu, Z. Y.; Fung, W. K.: Estimation in a semiparametric model for longitudinal data with unspecified dependence structure, Biometrika 89, 579-590 (2002) · Zbl 1036.62035 · doi:10.1093/biomet/89.3.579
[6]Hu, X.; Wang, Z.; Zhao, Z.: Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models, Statist. probab. Lett. 79, 1044-1052 (2009) · Zbl 1158.62030 · doi:10.1016/j.spl.2008.12.011
[7]Huang, Z., Zhang, R., 2009. Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models. Statist. Probab. Lett., in press (doi:10.1016/j.spl.2009.05.008)
[8]Leng, C.: A simple approach for varying-coefficient model selection, J. statist. Plann. inference 139, 2138-2146 (2009) · Zbl 1160.62067 · doi:10.1016/j.jspi.2008.10.009
[9]Li, Q.; Huang, C. J.; Li, D.; Fu, T. T.: Semiparametric smooth coefficient models, J. bus. Econom. statist. 20, 412-422 (2002)
[10]Li, R.; Liang, H.: Variable selection in semiparametric regression modeling, Ann. statist. 36, 261-286 (2008) · Zbl 1132.62027 · doi:10.1214/009053607000000604 · doi:euclid:aos/1201877301
[11]Schumaker, L. L.: Spline functions, (1981) · Zbl 0449.41004
[12]Stone, C. J.: Optimal global rates of convergence for nonparametric regression, Ann. statist. 10, 1348-1360 (1982) · Zbl 0511.62048 · doi:10.1214/aos/1176345969
[13]Tibshirani, R.: Regression shrinkage and selection via the LASSO, J. roy. Stat. soc. Ser. B 58, 267-288 (1996) · Zbl 0850.62538
[14]Wang, L.; Chen, G.; Li, H.: Group SCAD regression analysis for microarray time course gene expression data, Bioinformatics 23, 1486-1494 (2007)
[15]Wang, L.; Li, H.; Huang, J. Z.: Variable selection in nonparametric varying-coefficient models for analysis of repeated measurements, J. amer. Statist. assoc. 103, 1556-1569 (2008)
[16]Wang, H.J., Zhu, Z., Zhou, J., 2009. Quantile regression in partially linear varying coefficient models. Ann. Statist. (in press)
[17]You, J. H.; Zhou, Y.: Empirical likelihood for semiparametric varying-coefficient partially linear regression models, Statist. probab. Lett. 76, 412-422 (2006) · Zbl 1086.62057 · doi:10.1016/j.spl.2005.08.029
[18]Zhang, W.; Lee, S. Y.; Song, X.: Local polynomial Fitting in semivarying coefficient models, J. multivariate anal. 82, 166-188 (2002) · Zbl 0995.62038 · doi:10.1006/jmva.2001.2012
[19]Zou, H.: The adaptive lasso and its oracle properties, J. amer. Statist. assoc. 101, 1418-1429 (2006) · Zbl 1171.62326 · doi:10.1198/016214506000000735