We construct bootstrap confidence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap confidence intervals are considered and compared. We find that the commonly used bootstrap percentile intervals are inferior to the T intervals an...

Linear independence of the blending functions is a necessary requirement for T-spline in isogeometric analysis. The main work this paper focuses on analysis about T-splines degree one, we demonstrate that all such one are linearly independent. advantage owned by it can avoid problem judging whether model analysis-suitable or not, especially occasions need quick response from results. This may p...

This paper describes a novel method to construct solid rational T-splines for complex genus-zero geometry from boundary surface triangulations. We first build a parametric mapping between the triangulation and the boundary of the parametric domain, a unit cube. After that we adaptively subdivide the cube using an octree subdivision, project the boundary nodes onto the input triangle mesh, and a...

In this paper, we introduce a new type of splines—polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local suppor...

In this article we propose to analyze over-dispersed panel count data using a Gamma-Frailty nonhomogeneous Poisson process model. Conditional on a Gamma distributed frailty variable, the cumulative count, N (t), is assumed to follow a nonhomogeneous Poisson process. Cubic B-spline functions are used to approximate the logarithm of the baseline mean function Λ0 (t) in the semiparametric proporti...

A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces Sm Δ and S t n Δ over a domain D with a partition Δ, the Bezout number BN m,r;n,t;Δ is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves f x, y 0 and g x, y 0, where f x, y ∈ Sm Δ and g x, y ∈ Sn Δ . In ...

The multiplicity of a zero of a (univariate, polynomial) spline is defined in terms of its B-spline coefficients, thus making certain bounds trivial while, at the same time, adhering to the principle that the multiplicity of a zero indicates the number of simple zeros nearby achievable by a nearby element from the same class. In particular, the multiplicity depends on the class to which the fun...