Citation: | ZENG Jie, CHENG Weihu, CHEN Haiqing. Model Averaging for Varying Coefficient Partially Linear Models With Missing Data[J]. Journal of Beijing University of Technology, 2019, 45(4): 405-412. DOI: 10.11936/bjutxb2017120029 |
This paper is centered on model selection and model averaging procedure in varying coefficient partially linear models when the responses are missing at random. Under the misspecification framework, the focused information criterion (FIC) and the frequentist model average (FMA) estimator were developed based on the imputation method and the Profile least-squares technique. Then, theoretical properties of the FIC and FMA were examined. The simulation studies demonstrate the superiority of the proposed method and the approach will be applied to CD4 data.
[1] |
FAN J Q, HUANG T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models[J]. Bernoulli, 2005, 11(6):1031-1057. doi: 10.3150/bj/1137421639
|
[2] |
AHMAD I, LEELAHANON S, LI Q. Efficient estimation of a semiparametric partially linear varying coefficient model[J]. The Annals of Statistics, 2005, 33(1):258-283. doi: 10.1214/009053604000000931
|
[3] |
李志强, 薛留根.缺失数据下的半参数变系数模型的借补估计[J].应用数学学报, 2009, 32(3):422-430. doi: 10.3321/j.issn:0254-3079.2009.03.004
LI Z Q, XUE L G. The imputation estimators of semiparametric varying-coefficient models with missing data[J]. Acta Mathematicae Applicatae Sinica, 2009, 32(3):422-430. (in Chinese) doi: 10.3321/j.issn:0254-3079.2009.03.004
|
[4] |
赵培信, 薛留根.响应变量随机缺失下的变系数部分线性模型的经验似然推断[J].工程数学学报, 2010, 27(5):771-780. doi: 10.3969/j.issn.1005-3085.2010.05.002
ZHAO P X, XUE L G. Empirical likelihood inferences for semiparametric varying coefficient partially linear models with missing responses at random[J]. Chinese Journal of Engineering Mathematics, 2010, 27(5):771-780. (in Chinese) doi: 10.3969/j.issn.1005-3085.2010.05.002
|
[5] |
AKAIKE H. Maximum likelihood identification of Gaussian autoregressive moving average models[J]. Biometrika, 1973, 60(2):255-265. doi: 10.1093/biomet/60.2.255
|
[6] |
SCHWARZ G. Estimating the dimension of a model[J]. The Annals of Statistics, 1978, 6(2):461-464. doi: 10.1214/aos/1176344136
|
[7] |
MALLOWS C L. Some comments on Cp[J]. Technometrics, 1973, 15(4):661-675. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0215750933/
|
[8] |
TIBSHIRANI R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society:Series B, 1996, 58(1):267-288. http://d.old.wanfangdata.com.cn/OAPaper/oai_pubmedcentral.nih.gov_3410531
|
[9] |
BUCKLAND S T, BURNHAM K P, AUGUSTIN N H. Model selection:an integral part of inference[J]. Biometrics, 1997, 53(2):603-618. doi: 10.2307/2533961
|
[10] |
CLAESKENS G, HJORT N L. The focused information criterion[J]. Journal of the American Statistical Association, 2003, 98(464):900-916. doi: 10.1198/016214503000000819
|
[11] |
HJORT N L, CLAESKENS G. Frequentist model average estimators (with discussion)[J]. Journal of the American Statistical Association, 2003, 98:879-945. doi: 10.1198/016214503000000828
|
[12] |
HJORT N L, CLAESKENS G. Focussed information criteria and model averaging for Cox's hazard regression model[J]. Journal of the American Statistical Association, 2006, 101(476):1449-1464. doi: 10.1198/016214506000000069
|
[13] |
ZHANG X Y, LIANG H. Focused information criterion and model averaging for generalized additive partial linear models[J]. The Annals of Statistics, 2011, 39(1), 174-200. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1103.1480
|
[14] |
WANG H Y, ZOU G H, WAN A T K. Model averaging for varying-coefficient partially linear measurement error models[J]. Electronic Journal of Statistics, 2012(6):1017-1039. http://mathscinet.ams.org/mathscinet-getitem?mr=2988437
|
[15] |
DU J, ZHANG Z Z, XIE T F. Focused information criterion and model averaging in censored quantile regression[J]. Metrika, 2017, 80(5):547-570. doi: 10.1007/s00184-017-0616-1
|
[16] |
SUN Z M, SUN L Q, LU X L, et al. Frequentist model averaging estimation for the censored partial linear quantile regression model[J]. Journal of Statistical Planning and Inference, 2017(189):1-15. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=5268bbf6f2fbc037c7f449e0f885b982
|
[17] |
王海鹰, 邹国华.线性测量误差模型的平均估计[J].系统科学与数学, 2012, 32(1):1-14. http://d.old.wanfangdata.com.cn/Periodical/xtkxysx-zw201201001
WANG H Y, ZOU G H. Frequentist model average estimation for linear errors-in-variables models[J]. Journal of Systems Science and Mathematical Sciences, 2012, 43(7):1-14. (in Chinese) http://d.old.wanfangdata.com.cn/Periodical/xtkxysx-zw201201001
|
[18] |
FAN J Q, ZHANG J T. Two-step estimation of functional linear models with applications to longitudinal data[J]. Journal of the Royal Statistical Society:Series B, 2000, 62(2):303-322. doi: 10.1111/rssb.2000.62.issue-2
|
[19] |
FAN J Q, LI R Z. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis[J]. Journal of the American Statistical Association, 2004, 99(467):710-723. doi: 10.1198/016214504000001060
|
[20] |
HUANG J H, WU C O, ZHOU L. Varying-coefficient models and basis function approximations for the analysis of repeated measurements[J]. Biometrika, 2002, 89(1):111-128. doi: 10.1093/biomet/89.1.111
|
[21] |
HANSEN B E. Least squares model averaging[J]. Econometrica, 2007, 75(4):1175-1189. doi: 10.1111/ecta.2007.75.issue-4
|
[22] |
LIANG H, ZOU G H, WAN A T K, et al. Optimal weight choice for frequentist model average estimators[J]. Journal of the American Statistical Association, 2011, 106(495):1053-1066. doi: 10.1198/jasa.2011.tm09478
|
[23] |
HANSEN B E, RACINE J. Jackknife model averaging[J]. Journal of Econometrics, 2012, 167(1):38-46. doi: 10.1016/j.jeconom.2011.06.019
|
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