BaseNorm: Normalized spline basis

In pkmon: Least-Squares Estimator under k-Monotony Constraint for Discrete Functions

Normalized spline basis

Description

Computes the k-monotone discrete splines from Lefevre and Loisel (2013).

Usage

BaseNorm(k, J)

Arguments

k	Degree of monotony
J	maximum support of the splines

Value

matrix Q with J+1 rows and J+1 columns with Q(i,j)=Q_j^k(i-1)=C_{j-i+k-1}^{k-1}, where C represents the binomial coefficient.

Author(s)

Jade Giguelay

References

Giguelay, J., (2016), Estimation of a discrete distribution under k-monotony constraint, in revision, (arXiv:1608.06541)

Lefevre C., Loisel S. (2013) <DOI:10.1239/jap/1378401239> On multiply monotone distributions, continuous or discrete, with applications, Journal of Applied Probability, 50, 827–847.

See Also

rSpline, dSpline, rmixSpline, dmixSpline

Examples

# Computing 3-monotone splines with maximum support 8
Q=BaseNorm(3, 8)
matplot(Q, type="l", main="3-monotone splines with maximum support 8");

pkmon documentation built on Aug. 28, 2023, 5:06 p.m.