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...

We extend the classical Budan-Fourier theorem to Hermite-Birkhoff splines, that is splines whose knots are determined by a finite incidence matrix. This is then applied to problems of interpolation by Hermite-Birkhoff splines, where the nodes of interpolation are also determined by a finite incidence matrix. For specified knots and nodes in a finite interval, conditions are examined under which...

In many statistical applications, nonparametric modeling can provide insights into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from classical tools for parametric modeling. For example, stepwise variable selection with spline basis terms is ...

(1) inf{‖f ‖p : f ∈ C [0, 1], f(ti) = ei, i = 1, . . . , m}, where ‖ · ‖p is the usual L [0, 1] norm, 1 ≤ p ≤ ∞, and to characterize f for which the above infimum is attained. If m ≤ n, then this problem has a simple solution. There are algebraic polynomials of degree at most n−1 satisfying the interpolation data, and any of these polynomials obviously solve our problem. If m > n then, in gener...

The paper deals with modeling of human head surface on the basis of quadratic triangular B-splines for the standard videocodec MPEG-4 SNHC. First, we define a triangular B-spline surface of any degree and then we present its calculation for modeling of the quadratic form. Next, we apply the quadratic triangular B-splines on modeling of the human head surface using 3D polygonal model Candide 3-1...

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by definition curves over stations, bow and stern contours plan lines. Thus, new knots are created applying an equal spaced subdivision on defined B-spline Then, these transversal space knots, longitudinal subdivided into equally too. Subsequently, knots. Finally,...

Generalized additive models (GAMs) have become an elegant and practical option in model building. Estimation of a smooth GAM component traditionally requires an algorithm that cycles through and updates each smooth, while holding other components at their current estimated fit, until specified convergence. We aim to fit all the smooth components simultaneously. This can be achieved using penali...

We examine a test of a nonparametric regression function based on penalized spline smoothing. We show that, similarly to a penalized spline estimator, the asymptotic power of the penalized spline test falls into a small- K or a large-K scenarios characterized by the number of knots K and the smoothing parameter. However, the optimal rate of K and the smoothing parameter maximizing power for tes...

This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smo...