estimate_sigma: Perform an estimation of the standard deviation of the noise.

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

Perform an estimation of the standard deviation of the noise.

Description

This function performs an estimation of the standard deviation of the noise in the curves. The following formula is used:

\hat{σ^2} = \frac{1}{N}∑_{n = 1}^{N} \frac{1}{2(M_n - 1)}∑_{l = 2}^{M_n}(Y_{n, (l)} - Y_{n, (l-1)})^2

Usage

estimate_sigma(curves, delta = 0.1)

Arguments

curves	List, where each element represents a curve. Each curve have to be defined as list with two entries: $t Sampling points. $x Observed points.
delta	Numeric (default = 0.1), neighborhood for the estimation.

Value

Numeric, estimation of the std of the noise σ

References

S. Golovkine, N. Klutchnikoff, V. Patilea (2020) - Learning the smoothness of noisy curves with application to online curve estimation.

StevenGolovkine/funestim documentation built on June 15, 2022, 3:42 a.m.