Abstract
This paper considers the testing problem of partially linear models with missing covariates. The inverse probability weighted restricted estimator for the parametric component under linear constraint is derived and proven to share asymptotically normal distribution. To test the linear constraint, we construct two test statistics based on the the Lagrange multiplier and the empirical likelihood methods. The limiting distributions of the resulting test statistics are both standard chi-squared distributions under the null hypothesis. Simulation studies and a real data analysis are conducted to illustrate relevant performances.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
12 September 2019
Unfortunately, due to a technical error, the articles published in issues 60:2 and 60:3 received incorrect pagination. Please find here the corrected Tables of Contents. We apologize to the authors of the articles and the readers.
References
Engle R, Granger C, Rice J, Weiss A (1986) Semiparametric estimates of the relation between weather and electricity sales. J Am Stat Assoc 81:310–319
Fan JQ, Huang T (2005) Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli 11:1031–1057
Härdle W, Liang H, Gao JT (2000) Partially linear models. Physica-Verlag, Heidelberg
Liang H (2008) Generalized partially linear models with missing covariates. J Multivar Anal 99:880–895
Liang H, Qin YS (2008) Empirical likelihood-based inference for partially linear models with missing covariates. Aust N Z J Stat 50:347–359
Liang H, Wang SJ, Robbins JM, Carroll RJ (2004) Estimation in partially linear models with missing covariates. J Am Stat Assoc 99:357–367
Liu XH, Wang Z, Hu XM (2011) Testing heteroscedasticity in partially linear models with missing covariates. J Nonparametr Stat 23:321–337
Qin J, Lawless J (1994) Empirical likelihood and general estimating equations. Ann Stat 22:300–325
Qin G, Zhu Z, Fung WK (2012) Robust estimation of the generalised partial linear model with missing covariates. J Nonparametr Stat 24:517–530
Rubin DB (1976) Inference and missing data. Biometrika 63(3):581–592
Shi J, Zhao F (2016) Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition. Stat Pap. doi:10.1007/s00362-016-0773-8
Sun J, Sun QH (2015) An improved and efficient estimation method for varying-coefficient model with missing covariates. Stat Probab Lett 107:296–303
Tang LJ, Zhou ZG (2015) Weighted local linear CQR for varying-coefficient models with missing covariates. TEST 24:583–604
Wang QH (2009) Statistical estimation in partial linear models with covariate data missing at random. Ann Inst Stat Math 61:47–84
Wang QH, Sun ZH (2007) Estimation in partially linear models with missing responses at random. J Multivar Anal 98:1470–1493
Wang QH, Linton O, Härdle W (2004) Semiparametric regression analysis with missing response at random. J Am Stat Assoc 99:334–345
Wei CH (2012) Statistical inference for restricted partially linear varying coefficient errors-in-variables models. J Stat Plan Inference 42:2464–2472
Wei CH, Wu XZ (2008) Profile Lagrange multiplier test for partially linear varying-coefficient regression models. J Syst Sci Math Sci 28:416–424
Wu L, Wu H (2002) Nonlinear mixed-effect models with missing time-dependent covariates with application to HIV viral dynamics. J R Stat Soc Ser C 51:297–318
Xue LG, Xue D (2011) Empirical likelihood for semiparametric regression model with missing response data. Journal of Multivariate Analysis 102:723–740
Zhang WW, Li GR, Xue LG (2011) Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition. Comput Stat Data Anal 55:3027–3040
Acknowledgements
The authors thank the Editor and referees for the helpful comments and suggestions which greatly improved the paper. The Project Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15A010019).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, Z., Tang, L. Testing for parametric component of partially linear models with missing covariates. Stat Papers 60, 747–760 (2019). https://doi.org/10.1007/s00362-016-0848-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-016-0848-6