estimate_risk: Perform an estimation of the risk on a set of curves at a...

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

Description

This function performs the estimation of the risk on a set of curves at a particular sampling points t_0. Both the real and estimated curves have to be sampled on the same grid.

Usage

estimate_risk(curves, curves_estim, t0_list = 0.5)

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.
t0_list	A vector of numerics, sampling points where the risk will be computed. Can have a single value.

Details

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

MeanRSE(t_0) = \frac{1}{N}∑_{n = 1}^{N}(X_n(t_0) - \hat{X}_n(t_0))^2

and

MeanRSE(t_0) = \max_{1 ≤q n ≤q N} (X_n(t_0) - \hat{X}_n(t_0))^2

Value

A list, with the mean and max 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_risk(X, X_smoothed, t0_list = 0.5)

## End(Not run)

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