Free-knot Splines and Adaptive Knot Selection
نویسندگان
چکیده
منابع مشابه
Convexity Preserving Approximation by Free Knot Splines
In this paper we study the order of shape preserving approximation of functions f in Sobolev space by free knot splines. The main result is that we can preserve k-convexity of f for general k, and retain the optimal order of approximation n ?r at the same time.
متن کاملMdl Knot Selection for Penalized Splines
There exists a well known connection between penalized splines and mixed models. This connection makes it possible to exploit certain results derived for mixed models in the estimation of penalized splines. We have derived the Minimum Description Length (MDL) model selection criterion [1] for mixed models (see eg. [2]). In this paper we investigate the performance of the MDL criterion in fittin...
متن کاملFree-Knot Polynomial Splines with Confidence Intervals
We construct approximate confidence intervals for a nonparametric regression function, using polynomial splines with free-knot locations. The number of knots is determined by generalized cross-validation. The estimates of knot locations and coefficients are obtained through a non-linear least squares solution that corresponds to the maximum likelihood estimate. Confidence intervals are then con...
متن کاملSplines and unsorted knot sequences
The definition of a B-spline is extended to unordered knot sequences. The added flexibility implies that the resulting piecewise polynomials, named U-splines, can be negative and locally linearly dependent. It is therefore remarkable that linear combinations of U-splines retain many properties of splines in B-spline form including smoothness, polynomial reproduction, and evaluation by recurrence.
متن کاملKnot insertion for Natural Splines
We derive knot insertion formulas for the B-spline basis for natural splines. We also show that this basis is totally positive and give necessary and su cient nesting conditions for uniqueness of interpolation. x
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: JOURNAL OF THE JAPAN STATISTICAL SOCIETY
سال: 2005
ISSN: 1348-6365,1882-2754
DOI: 10.14490/jjss.35.303