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

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

Description

This function performs an estimation of the standard deviation of the noise in the curves. Based on add ref, 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(data, t0 = 0.5, k0 = 2)

Arguments

data	A list, where each element represents a curve. Each curve have to be defined as a list with two entries: $t The sampling points $x The observed points.
t0	Numeric, the sampling point at which we estimate σ. We will consider the 8k0 - 7 nearest points of t_0 for the estimation of σ
k0	Numeric, the number of neighbors of t_0 to consider. Should be set as k0 = M * exp(-log(log(M))^2).

Value

Numeric, an estimation of the standard deviation of the noise.

Examples

df <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
estimate_sigma(df, t0 = 0.5, k0 = 14)

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