Description Usage Arguments Details Value Author(s) Source References See Also Examples
This function provides an estimate of the non-parametric regression function with a shape constraint of convexity and a smoothness constraint via a Lipschitz bound.
1 2 3 4 5 6 7 8 9 |
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 x; Defaults to all elements 1/n. |
L |
a numeric value providing the Lipschitz bound on the function. |
... |
additional arguments. |
x |
an object of class ‘cvx.lip.reg’. |
object |
An object of class ‘cvx.lip.reg’. |
newdata |
a matrix of new data points in the predict function. |
deriv |
a numeric either 0 or 1 representing which derivative to evaluate. |
The function minimizes
∑_{i=1}^n w_i(z_i - θ_i)^2
subject to
-L≤\frac{θ_2 - θ_1}{t_2 - t_1}≤\cdots≤\frac{θ_n - θ_{n-1}}{t_n - t_{n-1}}≤ L
for sorted t values and z reorganized such that z_i corresponds to the new sorted t_i. This function uses the nnls
function from the nnls
package to perform the constrained minimization of least squares. plot
function provides the scatterplot along with fitted curve; it also includes some diagnostic plots for residuals. Predict function now allows calculating the first derivative also.
An object of class ‘cvx.lip.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’. |
residuals |
residuals obtained from the fit. |
minvalue |
minimum value of the objective function attained. |
iter |
Always set to 1. |
convergence |
a numeric indicating the convergence of the code. |
Arun Kumar Kuchibhotla, arunku@wharton.upenn.edu.
Lawson, C. L and Hanson, R. J. (1995). Solving Least Squares Problems. SIAM.
Chen, D. and Plemmons, R. J. (2009). Non-negativity Constraints in Numerical Analysis. Symposium on the Birth of Numerical Analysis.
See also the function nnls
.
1 2 3 4 5 6 7 | args(cvx.lip.reg)
x <- runif(50,-1,1)
y <- x^2 + rnorm(50,0,0.3)
tmp <- cvx.lip.reg(x, y, L = 10)
print(tmp)
plot(tmp)
predict(tmp, newdata = rnorm(10,0,0.1))
|
Loading required package: nnls
Loading required package: cobs
function (t, z, w = NULL, L, ...)
NULL
Call:
cvx.lip.reg.default(t = x, z = y, L = 10)
Minimum Criterion Value Obtained:
[1] 0.08694414
Number of Iterations:
[1] 1
Convergence Status:
[1] 1
[1] 0.02043385 0.02322928 0.01831447 0.01756469 0.01985495 0.01956844
[7] 0.02832310 0.02218437 0.01964059 0.01893204
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