estimate_H0_deriv: Perform an estimation of H_0 when the curves are derivables

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

Description

This function performs an estimation of H_0 used for the estimation of the bandwidth for a univariate kernel regression estimator defined over continuous domains data in the case the curves are derivables.

Usage

estimate_H0_deriv(data, t0 = 0, eps = 0.01, k0 = 2, sigma = NULL)

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 points at which we estimate H_0. We will consider the 8k0 - 7 nearest points of t_0 for the estimation of H_0 when σ is unknown.
eps	Numeric, precision parameter. It is used to control how much larger than 1, we have to be in order to consider to have a regularity larger than 1 (default to 0.01).
k0	Numeric, the number of neighbors of t_0 to consider.
sigma	Numeric, true value of sigma. Can be NULL.

Value

Numeric, an estimation of H_0.

References

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

See Also

Other estimate H_0: estimate_H0_deriv_list(), estimate_H0_list(), estimate_H0()

Examples

X <- generate_integrate_fractional_brownian(N = 1000, M = 300,
                                            H = 0.5, sigma = 0.01)
estimate_H0_deriv(X, t0 = 0.5, eps = 0.01, k0 = 6)

StevenGolovkine/SmoothCurves documentation built on Nov. 14, 2021, 1:12 p.m.