S For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothi...

This thesis will focus on applying smoothing splines to magnetic resonance image (MRI) analysis. Some additional work on support vector machine with a hybrid loss function will be discussed. We apply smoothing splines to both the structural MRI and functional MRI. For the structural MRI, we fit thin plate splines to overlapping blocks of the image with different configurations of knots. The opt...

Splines have been investigated in 1970s as a basic tool of applied mathematics (de Boor, 1978), (Schumaker, 1981). The dynamic splines based on linear control theory were first used in trajectory planning by Crouch and collaborators (Crouch and Jackson, 1991). For statistical applications, an important result was made by Wahba (Wahba, 1990). Further, in a series of papers (Agwu and Martin, 1998...

We develop a method of constructing trivariate optimal smoothing splines using normalized uniform B-spline as the basis functions. Such splines are useful particularly for modeling dynamic shape of 3-dimensional deformable object by using two variables for 3D shape and one for time evolution. The trivariate splines are constructed as a tensor product of three B-splines, and an optimal smoothing...