Topics in Semiparametric Regression Estimation with Missing Covariates Using Single-Index Models
Abstract
Missing data are very common in many areas such as sociology, biomedical sciences and clinical
trials. Simply ignoring the incomplete cases may cause bias in estimation procedures. In
this dissertation we investigate semiparametric estimation of linear regression coefficients through
generalized estimating equations with single-index models when some covariates are missing at
random for both independent and identically distributed (i.i.d.) data and longitudinal data. Existing
popular semiparametric estimators by weighted estimating equations may run into difficulties
when some selection probabilities are small or the dimension of the covariates is not low.
For i.i.d. data, we propose a new simple parameter estimator using a kernel assisted estimator
for the augmentation by a single-index model without using the inverse of selection probabilities.
We explore the asymptotic efficiency of the proposed estimator and its relationships with existing
estimators. In particular, we show that under certain conditions the proposed estimator is as
efficient as the existing methods based on standard kernel smoothing, which are often practically
infeasible in the case of multiple covariates.
For incomplete longitudinal data, we propose a similar estimator when the covariate is nonmonotone
missing at random. Heteroscedasticity is considered and working independence correlation
structure is applied to simplify the estimation procedure. Asymptotic consistency and
normality are derived along with sandwich formulas for asymptotic covariances.
The above methods are supported by simulation studies and real data examples. The numerical
results show that the proposed estimators avoid some numerical issues caused by estimated small
selection probabilities that are needed in other estimators.
Subject
Missing dataLongitudinal data
Generalized estimating equation
Single-index model
Kernel estimation
Citation
Sun, Zhuoer (2018). Topics in Semiparametric Regression Estimation with Missing Covariates Using Single-Index Models. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /173893.