This thesis is concerned with problems arising when one wants to apply flexible non- parametric local regression models to data when there is additional qualitative in formation. It is also concerned with nonparametric regression problems involving interval-censored responses. These problems are studied via asymptotic theory where possible and by simulation.
Iterated conditional expectation methods and local likelihood estimation for nonparametric interval-censored regression are developed. Simulation results show that local likelihood estimation is often superior to local regression estimators when observations have been imputed using either interval midpoints or iterated conditional expectations when the censoring intervals are wide or of varying width. When the intervals are smaller and of fixed width, none of the imputation approaches dominate the others.
Constrained data sharpening for nonparametric regression is applied to new situations such as where constraints are defined by convexity, concavity, and in terms of differential operators. Data sharpening is compared with competing kernel methods in terms of bias, variance and MISE. It is proved that the constrained data sharpening estimator has the same rate of convergence as the constrained weighting estimator of Hall and Huang (2001). Also, penalized data sharpening is proposed as a new form of constrained data sharpening. The sharpened responses can be computed analytically which makes the method very convenient, both for studying theoretically and for applying practicall
