5 research outputs found
The transfer principle: A tool for complete case analysis
This paper gives a general method for deriving limiting distributions of
complete case statistics for missing data models from corresponding results for
the model where all data are observed. This provides a convenient tool for
obtaining the asymptotic behavior of complete case versions of established full
data methods without lengthy proofs. The methodology is illustrated by
analyzing three inference procedures for partially linear regression models
with responses missing at random. We first show that complete case versions of
asymptotically efficient estimators of the slope parameter for the full model
are efficient, thereby solving the problem of constructing efficient estimators
of the slope parameter for this model. Second, we derive an asymptotically
distribution free test for fitting a normal distribution to the errors.
Finally, we obtain an asymptotically distribution free test for linearity, that
is, for testing that the nonparametric component of these models is a constant.
This test is new both when data are fully observed and when data are missing at
random.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1061 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Model checking for partially linear models with missing responses at random
AbstractIn this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data
Model checking for partially linear models with missing responses at random
In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data.62F03 62G10 Model checking Response missing at random Imputation Inverse probability weighting Empirical process Re-sampling