| dc.description.abstract | Semiparametric regression has become very popular in the field of Statistics over the
years. While on one hand more and more sophisticated models are being developed,
on the other hand the resulting theory and estimation process has become more and
more involved. The main problems that are addressed in this work are related to
efficient inferential procedures in general semiparametric regression problems.
We first discuss efficient estimation of population-level summaries in general semiparametric
regression models. Here our focus is on estimating general population-level
quantities that combine the parametric and nonparametric parts of the model (e.g.,
population mean, probabilities, etc.). We place this problem in a general context,
provide a general kernel-based methodology, and derive the asymptotic distributions
of estimates of these population-level quantities, showing that in many cases the estimates
are semiparametric efficient.
Next, motivated from the problem of testing for genetic effects on complex traits in
the presence of gene-environment interaction, we consider developing score test in
general semiparametric regression problems that involves Tukey style 1 d.f form of
interaction between parametrically and non-parametrically modeled covariates. We
develop adjusted score statistics which are unbiased and asymptotically efficient and
can be performed using standard bandwidth selection methods. In addition, to over come the difficulty of solving functional equations, we give easy interpretations of the
target functions, which in turn allow us to develop estimation procedures that can be
easily implemented using standard computational methods.
Finally, we take up the important problem of estimation in a general semiparametric
regression model when covariates are measured with an additive measurement error
structure having normally distributed measurement errors. In contrast to methods
that require solving integral equation of dimension the size of the covariate measured
with error, we propose methodology based on Monte Carlo corrected scores to estimate
the model components and investigate the asymptotic behavior of the estimates.
For each of the problems, we present simulation studies to observe the performance of
the proposed inferential procedures. In addition, we apply our proposed methodology
to analyze nontrivial real life data sets and present the results. | en |
