Type: Package
Version: 1.0
Date: 2021-08-25
Title: The Computing of Monotonic Spline Bases and Constrained Least-Squares Estimates
Author: Yili Hong [aut, cre], Jie Min [aut, ctb]
Maintainer: Yili Hong <yilihong@vt.edu>
Description: Providing 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) <doi:10.1214/08-AOAS167>. The package also provides the computing of constrained least-squares estimates when a subset of or all of the regression coefficients are constrained to be non-negative.
License: GPL-2
NeedsCompilation: yes
Packaged: 2021-09-04 14:40:27 UTC; yilih
Repository: CRAN
Date/Publication: 2021-09-07 13:30:05 UTC

The Computing of Monotonic Spline Bases and Constrained Least-Squares Estimates

Description

The package 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). The package also provides the computing of constrained least-squares estimates when a subset of or all of the regression coefficients are constrained to be non-negative, as described in Fraser and Massam (1989).

References

Fraser, D. A. S. and H. Massam (1989). A mixed primal-dual bases algorithm for regression under inequality constraints. Application to concave regression. Scandinavian Journal of Statistics 16, 65-74.

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

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)

Constrained Least-Squares Estimates

Description

This function computes the constrained least-squares estimates when a subset of or all of the regression coefficients are constrained to be non-negative, as described in Fraser and Massam (1989).

Usage

clse(dat.obj)

Arguments

dat.obj

A list with the following format, list(y, mat, lam). Here y is the response vector, mat is the design matrix for the regression, and lam is a vector with the length that matches the number of columns in mat. The values of lam is either 0 or 1, with 0 means unconstrained and 1 means the corresponding regression coefficient is constrained to be non-negative.

Value

The returned value is a list with format, list(dat.obj, beta.vec, yhat). Here dat.obj is the input of the function, beta.vec gives the estimated regression coefficient, and yhat is the vector for the fitted response values.

References

Fraser, D. A. S. and H. Massam (1989). A mixed primal-dual bases algorithm for regression under inequality constraints. Application to concave regression. Scandinavian Journal of Statistics 16, 65-74.

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)
#generate the data object for the clse function.
dat.obj=list(y=y, mat=cbind(1, tmp$mat), lam=c(0, rep(1, ncol(tmp$mat))))
#fit clse.
fit=clse(dat.obj=dat.obj)
#visualize fitted results.
plot(x, y, pch=16)
lines(x, fit$yhat, lwd=3, col=2)