Partially informative normal and partial spline models

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] There is a well-known Bayesian interpretation of function estimation by spline smoothing using a limit of proper normal priors. This limiting prior has the same form with Partially Informative Normal (PIN), which was introduced in Sun et al. (1999). In this dissertation, we first discuss some properties of PIN. In terms of improper priors, we consider q-vague convergence as the convergence mode. Then, we apply the properties to several extensions of smoothing spline problems. Partial spline model, which contains a non-parametric part as regular smoothing spline together with a linear parametric part, is discussed. We perform simulation studies and applications on yield curves. Specifically, Nelson-Siege (NS) model is considered to construct the linear component. NS partial spline model is used for fitting single yield curve, while partial parallel and non-parallel spline models are used for multiple curves. Then, large p, small n regression problem associated with the generalized univariate smoothing spline, some studies on bin smoothing splines, adaptive smoothing splines and correlated smoothing splines are discussed.