simest (version 0.4)

cvx.pen.reg:

Description

This function provides an estimate of the non-parametric regression function with a shape constraint of convexity and smoothness constraint provided through square integral of second derivative.

Usage

cvx.pen.reg(x, y, lambda, w = NULL, tol = 1e-05, maxit = 1000,...)
# S3 method for default
cvx.pen.reg(x, y, lambda, w = NULL, tol = 1e-05, maxit = 1000,...)
# S3 method for cvx.pen.reg
plot(x,...)
# S3 method for cvx.pen.reg
print(x,...)
# S3 method for cvx.pen.reg
predict(object, newdata = NULL,...)

Arguments

x

a numeric vector giving the values of the predictor variable. For plot and print functions, x represents an object of class cvx.pen.reg.

y

a numeric vector giving the values of the response variable.

lambda

a numeric value giving the penalty value.

w

an optional numeric vector of the same length as x; Defaults to all 1.

maxit

an integer giving the maxmimum number of steps taken by the algorithm; defaults to 1000.

tol

a numeric providing the tolerance level for convergence.

...

any additional arguments.

object

An object of class `cvx.pen.reg'. This is for predict function.

newdata

a vector of new data points to be used in the predict function.

Value

An object of class `cvx.pen.reg', basically a list including the elements

x.values

sorted `x' values provided as input.

y.values

corresponding `y' 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.

alpha

a numeric vector of length 2 less than `x'. This represents the coefficients of the B-splines in the second derivative of the estimator.

AlphaMVal

a numeric vector needed for predict function.

lower

a numeric vector needed for predict function.

upper

a numeric vector needed for predict function.

Details

The function minimizes $$\sum_{i=1}^n w_i(y_i - f(x_i))^2 + \lambda\int\{f''(x)\}^2dx$$ subject to convexity constraint on \(f\). plot function provides the scatterplot along with fitted curve; it also includes some diagnostic plots for residuals. Predict function returns a matrix containing the inputted newdata along with the function values, derivatives and second derivatives.

Examples

args(cvx.pen.reg)
x <- runif(50,-1,1)
y <- x^2 + rnorm(50,0,0.3)
tmp <- cvx.pen.reg(x, y, lambda = 0.01)
print(tmp)
plot(tmp)
predict(tmp, newdata = rnorm(10,0,0.1))