estimate_risks: Perform an estimation of the risk on a set of curves along...

In StevenGolovkine/denoisr: Nonparametric Kernel Smoothing Methods for Functional Data

Description

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

Usage

estimate_risks(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.

Details

Actually, two risks are computed. They are defined as:

MeanIntRSE = \frac{1}{N}∑_{n = 1}^{N}\int(X_n(t) - \hat{X}_n(t))^2dt

and

MeanIntRSE = \max_{1 ≤q n ≤q N} \int(X_n(t) - \hat{X}_n(t))^2dt

Value

A list, with the mean and max integrated residual squared error in t_0.

Examples

## Not run: 
 X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
 X_smoothed <- smooth_curves(X)$smooth
 estimate_risks(X, X_smoothed)

## End(Not run)

StevenGolovkine/denoisr documentation built on Nov. 15, 2021, 8:44 a.m.