Perform an estimation of the risk on one curve along the sampling points.

This function performs the estimation of the risk on one curve along the sampling points. Both the real and estimated curve have to be sampled on the same grid.

estimate_int_risk(curves, curves_estim)

Arguments

curves	A list, where each element represents a real curve. Each curve have to be defined as a list with two entries: $t The sampling points $x The observed points.
curves_estim	A list, where each element represents an estimated curve. Each curve have to be defined as a list with two entries: $t The sampling points $x The estimated points.

curves

A list, where each element represents a real curve. Each curve have to be defined as a list with two entries:

$t The sampling points
$x The observed points.

curves_estim

A list, where each element represents an estimated curve. Each curve have to be defined as a list with two entries:

$t The sampling points
$x The estimated points.

Value

Numeric, the integrated mean squared error

Details

Actually, one risk is computed. They are defined as: $$IntRSE = \int(X_n(t) - \hat{X}_n(t))^2dt$$

Examples

if (FALSE) {
 X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
 X_smoothed <- smooth_curves(X)$smooth
 estimate_int_risk(X[[1]], X_smoothed[[1]])
}