Abstract
In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under the null and local alternative hypotheses are studied. Because the limiting null distribution is intractable, a Monte Carlo approach is applied to approximate the distribution to determine critical values. Simulation studies are carried out to examine the performance of our method, and a real data set from an environmental study is analyzed for illustration.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cheng P (1994) Nonparametric estimation of mean functionals with data missing at random. J Amer Statist Assoc 89: 81–87
Chiang CT, Rice JA, Wu CO (2001) Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J Amer Statist Assoc 96: 605–619
Fan J, Zhang JT (2000) Simultaneous confidence bands and hypothesis testing in varying–coefficient models. Scand J Stat 27: 715–731
Härdle W, Mammen E (1993) Comparing non-parametric versus parametric regression fits. Ann Statist 21: 1926–1947
Hastie T, Tibshirani R (1993) Varying–coefficient models. J R Statist Soc B 55: 757–796
Hoover DR, Rice JA, Wu CO, Yang LP (1998) Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85: 809–822
Huang JZ, Wu CO, Zhou L (2002) Varying–coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89: 111–128
Little RJA, Rubin DB (1987) Statistical analysis with missing data. Wiley, New York
Pollard D (1984) Convergence of stochastic processes. Springer, New York
Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70: 41–55
Sun ZH, Wang QH, Dai PJ (2009) Model checking for partially linear models with missing responses at random. J Multivar Anal 100: 636–651
Wang CY, Chen HY (2001) Augmented inverse probability weighted estimator for Cox missing covariate regression. Biometrics 57: 414–419
Wang Q, Rao JNK (2002) Empirical likelihood-based inference under imputation for missing response data. Ann Statist 30: 896–924
Wang QH, Lindon O, Härdle W (2004) Semiparametric regression analysis with missing response at random. J Amer Statist Assoc 99: 334–345
Wu CO, Chiang CT (2000) Kernel smoothing on varying–coefficient models with longitudinal dependent variable. Stat Sinica 10: 433–456
Xu WL, Zhu LX (2008) Goodness-of-fit testing for varying–coefficient models. Metrika 68: 129–146
Xu WL, Zhu LX (2009) A Goodness-of-fit test for a varying–coefficients model in longitudinal studies. J Nonparametric Stat 21: 427–440
Zhu LX (2005) Nonparametric Monte Carlo tests and their applications. Springer, New York
Zhu LX, Neuhaus G (2000) Nonparametric Monte Carlo tests for multivariate distributions. Biometrika 87: 919–928
Zhu LX, Ng KW (2003) Checking the adequacy of a partially linear model. Stat Sinica 13: 763–781
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, W., Zhu, L. Testing the adequacy of varying coefficient models with missing responses at random. Metrika 76, 53–69 (2013). https://doi.org/10.1007/s00184-011-0375-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-011-0375-3