| Title: | The Computing of Monotonic Spline Bases and Constrained Least-Squares Estimates |
|---|---|
| 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. |
| Authors: | Yili Hong [aut, cre], Jie Min [aut, ctb] |
| Maintainer: | Yili Hong <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0 |
| Built: | 2025-01-09 06:25:36 UTC |
| Source: | https://github.com/cran/MICsplines |
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).
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.
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).
clse(dat.obj)clse(dat.obj)
dat.obj |
A list with the following format, |
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.
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.
#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$yhat, lwd=3, col=2)#generate a dataset for illustration. x=seq(1,10,,100) y=x^2+rnorm(length(x)) #generate spline bases. tmp=MIC.splines.basis.fast(x=x, df = 10, knots = NULL, boundary.knots=NULL, type="Is",degree = 3,delta=0.001,eq.alloc=FALSE) #plot the spline bases. plot(tmp) #generate the data object for the clse function. dat.obj=list(y=y, mat=cbind(1, tmp$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)
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).
MIC.splines.basis.fast(x, df = NULL, knots = NULL, boundary.knots = NULL, type = "Ms", degree = 3, delta = 0.01, eq.alloc = FALSE)MIC.splines.basis.fast(x, df = NULL, knots = NULL, boundary.knots = NULL, type = "Ms", degree = 3, delta = 0.01, eq.alloc = FALSE)
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. |
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. |
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.
Meyer, M. C. (2008). Inference using shape-restricted regression splines. The Annals of Applied Statistics 2, 1013-1033.
#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 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)