Physical Sciences and Mathematics Commons^™

Joint Asymptotics For Smoothing Spline Semiparametric Nonlinear Models, Jiahui Yu

Doctoral Dissertations

We study the joint asymptotics of general smoothing spline semiparametric models in the settings of density estimation and regression. We provide a systematic framework which incorporates many existing models as special cases, and further allows for nonlinear relationships between the finite-dimensional Euclidean parameter and the infinite-dimensional functional parameter. For both density estimation and regression, we establish the local existence and uniqueness of the penalized likelihood estimators for our proposed models. In the density estimation setting, we prove joint consistency and obtain the rates of convergence of the joint estimator in an appropriate norm. The convergence rate of the parametric component …