BACKGROUND Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves ...

The objective of this study was to examine the feasibility of using random regression-spline (RR-spline) models for fitting growth traits in a multibreed beef cattle population. To meet the objective, the results from the RR-spline model were compared with the widely used multitrait (MT) model when both were fit to a data set (1.8 million records and 1.1 million animals) provided by the America...

A general setting is given for smooth interpolating splines depending on a parameter such that as this parameter approaches infinity the spline converges to the piecewise linear interpolant. The theory includes the standard exponential spline in tension, a rational spline, and several cubic splines. An algorithm is given for one of the cubics; the parameter for this example controls the spacing...

Motivated by the analysis of glomerular time series extracted from calciumimaging data, asymptotic theory for piecewise polynomial and spline regression with partially free knots and residuals exhibiting three types of dependence structures (long memory, short memory and anti-persistence) is considered. Unified formulas based on fractional calculus are derived for subordinated residual processe...

Estimates of variance components and genetic parameters for growth of Angus cattle from birth to 820 days of age were obtained from a random regression analysis. Trajectories were modelled through quadratic B-spline functions with 7 random regression coefficients for direct genetic and permanent environmental effects, and 5 coefficients for the corresponding maternal effects. Data comprised a l...

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

The local volatility function is approximated using two different models: a bicubic spline and High Dimensional Model Representation (HDMR) model. For a bicubic spline the local volatility values σi at a chosen discrete set of knots are determined by minimizing the least square error between market and model option prices. Model option prices are found using the one-factor diffusion process for...

B-spline curves are defined in a piecewise way over a closed interval, where the interval section points are called knots. In some recent publications geometrical properties of the modification of one knot value are discussed. The aim of this paper is to describe an effect of the symmetric modification of two knots.