cvx.lse.reg {simest} | R Documentation |
Convex Least Squares Regression.
Description
This function provides an estimate of the non-parametric regression function with a shape constraint of convexity and no smoothness constraint. Note that convexity by itself provides some implicit smoothness.
Usage
cvx.lse.reg(t, z, w = NULL,...)
## Default S3 method:
cvx.lse.reg(t, z, w = NULL, ...)
## S3 method for class 'cvx.lse.reg'
plot(x,...)
## S3 method for class 'cvx.lse.reg'
print(x,...)
## S3 method for class 'cvx.lse.reg'
predict(object, newdata = NULL, deriv = 0, ...)
Arguments
t |
a numeric vector giving the values of the predictor variable. |
z |
a numeric vector giving the values of the response variable. |
w |
an optional numeric vector of the same length as t; Defaults to all elements |
... |
additional arguments. |
x |
An object of class ‘cvx.lse.reg’. This is for plot and print function. |
object |
An object of class ‘cvx.lse.reg’. |
newdata |
a matrix of new data points in the predict function. |
deriv |
a numeric either 0 or 1 representing which derivative to evaluate. |
Details
The function minimizes
\sum_{i=1}^n w_i(z_i - \theta_i)^2
subject to
\frac{\theta_2 - \theta_1}{t_2 - t_1}\le\cdots\le\frac{\theta_n - \theta_{n-1}}{t_n - t_{n-1}}
for sorted t
values and z
reorganized such that z_i
corresponds to the new sorted t_i
. This function previously used the coneA
function from the coneproj
package to perform the constrained minimization of least squares. Currently, the code makes use of the nnls
function from nnls
package for the same purpose. plot
function provides the scatterplot along with fitted curve; it also includes some diagnostic plots for residuals. Predict function now allows computation of the first derivative.
Value
An object of class ‘cvx.lse.reg’, basically a list including the elements
x.values |
sorted ‘t’ values provided as input. |
y.values |
corresponding ‘z’ values in input. |
fit.values |
corresponding fit values of same length as that of ‘x.values’. |
deriv |
corresponding values of the derivative of same length as that of ‘x.values’. |
iter |
number of steps taken to complete the iterations. |
residuals |
residuals obtained from the fit. |
minvalue |
minimum value of the objective function attained. |
convergence |
a numeric indicating the convergence of the code. |
Author(s)
Arun Kumar Kuchibhotla, arunku@wharton.upenn.edu
Source
Lawson, C. L and Hanson, R. J. (1995). Solving Least Squares Problems. SIAM.
References
Chen, D. and Plemmons, R. J. (2009). Non-negativity Constraints in Numerical Analysis. Symposium on the Birth of Numerical Analysis.
Liao, X. and Meyer, M. C. (2014). coneproj: An R package for the primal or dual cone projections with routines for constrained regression. Journal of Statistical Software 61(12), 1 – 22.
Examples
args(cvx.lse.reg)
x <- runif(50,-1,1)
y <- x^2 + rnorm(50,0,0.3)
tmp <- cvx.lse.reg(x, y)
print(tmp)
plot(tmp)
predict(tmp, newdata = rnorm(10,0,0.1))