Abstract
This paper deals with estimation and test procedures for restricted linear errors-invariables (EV) models with nonignorable missing covariates. We develop a restricted weighted corrected least squares (WCLS) estimator based on the propensity score, which is fitted by an exponentially tilted likelihood method. The limiting distributions of the proposed estimators are discussed when tilted parameter is known or unknown. To test the validity of the constraints, we construct two test procedures based on corrected residual sum of squares and empirical likelihood method and derive their asymptotic properties. Numerical studies are conducted to examine the finite sample performance of our proposed methods.
Similar content being viewed by others
References
RJ Carroll, D Ruppert, L AStefanski, CMCrainiceanu. Measurement Error in Nonlinear Models, 2nd ed, Chapman and Hall, New York, 2006.
H Cui, S Chen. Empirical likelihood confidence region for parameter in the errors-in-variables models, J Multivariate Anal, 2003, 84(1): 101–115.
WA Fuller. Measurement Error Models, Wiley, New York, 1987.
D Jiang, P Zhao, N Tang. A propensity score adjustment method for regression models with nonignorably missing covariates, Comput Statist Data Anal, 2016, 94: 98–119.
JK Kim, CL Yu. A semiparametric estimation of mean functionals with nonignorable missing data, J Amer Statist Assoc, 2011, 106: 157–165.
H Liang, W Hardle, RJ Carroll. Estimation in a semiparametric partially linear errors-in-variables model, Ann Statist, 1999, 27: 1519–1935.
H Liang. Generalized partially linear models with missing covariates, J Multivariate Anal, 2008, 99: 880–895.
L Li, T Greene. Varying coefficients model with measurement error, Biometrics, 2008, 64: 519–526.
RJ ALittle, DB Rubin. Statistical Analysis with Missing Data, 2nd ed, Wiley, New York, 2002.
Z Ning, L Tang. Estimation and test procedures for composite quantile regression with covariates missing at random, Statist Probab Lett, 2014, 95: 15–25.
C Niu, X Guo, W Xu, et al. Empirical likelihood inference in linear regression with nonignorable missing response, Comput Statist Data Anal, 2014, 79: 91–112.
A Owen. Empirical likelihood ratio confidence intervals for single functional, Biometrika, 1988, 75: 237–249.
J Qin, J Lawless. Empirical likelihood and general estimating equations, Ann Statist, 1994, 22: 300–325.
JN KRao, AJ Scott. The analysis of categorical data from complex sample surveys: chi-squares tests for goodness of fit and independence in two-way tables, J Amer Statist Assoc, 1981, 76: 221–230.
JM Robins, A Rotnitsky, LP Zhao. Estimation of regression coefficients when some regressors are not always observed, J Amer Statist Assoc, 1994, 89: 846–866.
J Shao, L Wang. Semiparametric inverse propensity weighting for nonignorable missing data, Biometrika, 2016, 103: 175–187.
N Tang, P Zhao, H Zhu. Empirical likelihood for estimating equations with nonignorably missing data, Statist Sinica, 2014, 24: 723–747.
L Tang, Z Zhou. Weighted local linear CQR for varying coefficient models with missing covariates, TEST, 2015, 24: 583–604.
A ATsiatis. Semiparametric theory and missing data, Technometrics, 2007, 49: 228–229.
X LWang, F Chen, L Lin. Empirical likelihood inference for estimating equation with missing data, Sci China Math, 2013, 56: 1233–1245.
C Wei. Statistical inference for restricted partially linear varying coefficient errors-in-variables models, J Statist Plann Inference, 2012, 142: 2464–2472.
H Wong, S Guo, M Chen. On locally weighted estimation and hypothesis testing on varying coefficient models, J Statist Plann Inference, 2009, 139: 2933–2951.
L Xue. Empirical likelihood confidence interval for response mean with data missing at random, Scand J Statist, 2009, 36: 671–685.
H Yang, H Liu. Penalized weighted composite quantile estimators with missing covariates, Statist Papers, 2016, 57: 69–88.
H Yang, X Xia. Equivalence of two tests in varying coefficient partially linear errors in variable model with missing responses, J Korean Statist Soc, 2014, 43: 79–90.
J You, G Chen. Estimation of a semiparametric varying-coefficient partially linear errors-invariables model, J Multivariate Anal, 2006, 97: 324–341.
Y Zhou, T Alan, Y Wan. Combining least-squares and quantile regressions, J Statist Plann Inference, 2011, 141: 3814–3828.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Zhejiang Provincial Natural Science Foundation of China (LY15A010019), and National Natural Science Foundation of China (11501250).
Rights and permissions
About this article
Cite this article
Tang, Lj., Zheng, Sc. & Zhou, Zg. Estimation and test of restricted linear EV model with nonignorable missing covariates. Appl. Math. J. Chin. Univ. 33, 344–358 (2018). https://doi.org/10.1007/s11766-018-3550-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11766-018-3550-8