Smoothing Splines and Rank Structured Matrices: Revisiting the Spline Kernel

On Mixed Interpolating-Smoothing Splines and the ν-Spline

Unitary rank structured matrices

In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of unitary or Givens transformations. We provide also some basic operations for manipulating the representation, such as the transition to zerocreating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of ...

Efficient and fast spline-backfitted kernel smoothing of additive models

A great deal of effort has been devoted to the inference of additive model in the last decade. Among existing procedures, the kernel type are too costly to implement for high dimensions or large sample sizes, while the spline type provide no asymptotic distribution or uniform convergence. We propose a one step backfitting estimator of the component function in an additive regression model, usin...

Rank structured matrices: theory, algorithms and applications

In numerical linear algebra much attention has been paid to matrices that are sparse, i.e., containing a lot of zeros. For example, to compute the eigenvalues of a general dense symmetric matrix, this matrix is first reduced to a similar tridiagonal one using an orthogonal similarity transformation. The subsequent QR-algorithm performed on this n×n tridiagonal matrix, takes the sparse structure...

Spline-backfitted kernel smoothing of partially linear additive model

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate ...