ABSTRACT The objective of this study was to estimate the components variance and genetic parameters test-day milk yield in first lactation Girolando cows, using a random regression model. A total 126,892 (TDMY) records 15,351 first-parity Holstein, Gyr, breed cows were used, obtained from Associação Brasileira dos Criadores de Girolando. To (co) variance, additive functions permanent environmen...

Estimates of direct and maternal genetic parameters in beef cattle were obtained with a random regression model with a linear spline function (SFM) and were compared with those obtained by a multitrait model (MTM). Weight data of 18,900 Gelbvieh calves were used, of which 100, 75, and 17% had birth (BWT), weaning (WWT), and yearling (YWT) weights, respectively. The MTM analysis was conducted wi...

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...

INTRODUCTION The extent of viral replication during acute HIV infection (AHI) influences HIV disease progression. However, information comparing viral load (VL) kinetics with and without antiretroviral therapy (ART) in AHI is limited. The knowledge gained could inform preventive strategies aimed at reducing VL during AHI and therapeutic strategies to alter the viral kinetics that may enhance th...

We derive rate of convergence for spline regression under weak conditions. The results improve upon those in Huang (Ann. Statist. 26 (1998a) 242) in two ways. Firstly, results are obtained under less stringent conditions on the growing rate of the number of knots. Secondly, L2 approximation instead of L∞ approximation by splines are used to bound the rate of convergence, this allows us to obtai...

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...

Estimation of monotone functions has broad applications in statistics, engineering, and science. This paper addresses asymptotic behaviors of monotone penalized spline estimators using constrained dynamical optimization techniques. The underlying regression function is approximated by a B-spline of an arbitrary degree subject to the first-order difference penalty. The optimality conditions for ...