bspline_basis-class: b-spline basis

In MECfda: Scalar-on-Function Regression with Measurement Error Correction

b-spline basis

Description

A s4 class that represents a b-spline basis \{B_{i,p}(x)\}_{i=-p}^{k} on the interval [t_0,t_{k+1}], where B_{i,p}(x) is defined as

B_{i,0}(x) = \left\{ \begin{aligned} &I_{(t_i,t_{i+1}]}(x), & i = 0,1,\dots,k\\ &0, &i<0\ or\ i>k \end{aligned} \right.

B_{i,r}(x) = \frac{x - t_{i}}{t_{i+r}-t_{i}} B_{i,r-1}(x) + \frac{t_{i+r+1} - x} {t_{i+r+1} - t_{i+1}}B_{i+1,r-1}(x)

For all the discontinuity points of B_{i,r} (r>0) in the interval (t_0,t_k), let the value equals its limit, which means

B_{i,r}(x) = \lim_{t\to x} B_{i,r}(t)

Slots

Boundary.knots

boundary of the domain of the splines (start and end), which is t_0 and t_{k+1}. Default is [0,1]. See Boundary.knots in bs.

knots

knots of the splines, which is (t_1,\dots,t_k), equally spaced sequence is chosen by the function automatically with equal space (t_j = t_0 + j\cdot\frac{t_{k+1}-t_0}{k+1}) when not assigned. See knots in bs.

intercept

Whether an intercept is included in the basis, default value is TRUE, and must be TRUE. See intercept bs.

df

degree of freedom of the basis, which is the number of the splines, equal to p+k+1. By default k = 0, and df = p+1. See df bs.

degree

degree of the splines, which is the degree of piecewise polynomials p, default value is 3. See degree in bs.

Author(s)

Heyang Ji

Examples

bsb = bspline_basis(
            Boundary.knots = c(0,24),
            intercept      = TRUE,
            df             = NULL,
            degree         = 3
)

MECfda documentation built on April 3, 2025, 10:07 p.m.