MIC.splines.basis.fast {MICsplines}

Generating MIC Spline Bases

Description

This function provides C implementation for the computing of monotonic spline bases, including M-splines, I-splines, and C-splines, denoted by MIC splines. The definitions of the spline bases are described in Meyer (2008).

Usage

MIC.splines.basis.fast(x, df = NULL, knots = NULL, boundary.knots = NULL, 
type = "Ms", degree = 3, delta = 0.01, eq.alloc = FALSE)

Arguments

x

A numeric vector for the data to generate spline bases for.

df

The degree of freedom, which equals to the number of interior knots plus the spline degree.

knots

A vector for the interior knots.

boundary.knots

The values for the left and right boundary points.

type

The type of splines to be computed. "Ms" stands for M-splines, "Is" stands for I-splines, "IsN" stands for I-splines without normalization, and "Cs" stands for C-splines.

degree

The degree for the M-splines. I-splines are based on the integration of the M-splines, and C-splines are based on the integration of the I-splines.

delta

A numeric value that is used to set the bin width for numerical integration. Usually it is set to a small number.

eq.alloc

A logic variable, which is true if using equal spacing for the interior knots, and is false if using equal quantiles for the interior knots.

Value

A list with format, list(mat, x, ...). Here mat is the matrix for the spline bases, x is the vector for the data, and the rest of the items are carrying the information from the arguments.

References

Meyer, M. C. (2008). Inference using shape-restricted regression splines. The Annals of Applied Statistics 2, 1013-1033.

Examples

#generate a dataset for illustration.
x=seq(1,10,,100)
y=x^2+rnorm(length(x))
#generate spline bases.
tmp=MIC.splines.basis.fast(x=x, df = 10, knots = NULL, boundary.knots=NULL,
type="Is",degree = 3,delta=0.001,eq.alloc=FALSE)
#plot the spline bases.
plot(tmp)