estimate_H0_deriv_list: Perform an estimation of H_0 given a list of t_0 when the...

In StevenGolovkine/denoisr: 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 using the method of Golovkine et al. (2020) in the case the curves are derivables.

Usage

estimate_H0_deriv_list(data, t0_list, eps = 0.01, k0_list = 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_list	A vector of numerics, the sampling points at which we estimate H0. We will consider the 8k0 - 7 nearest points of t_0 for the estimation of H_0 when σ is unknown. Be careful not to consider t_0 close to the bound of the interval because local polynomials do not behave well in this case.
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). Should be set as ε = log^{-2}(M) .
k0_list	A vector of numerics, the number of neighbors of t_0 to consider. Should be set as k0 = M * exp(-log(log(M))^2) . We can set a different k_0, but in order to use the same for each t_0, just put a unique numeric.
sigma	Numeric, true value of sigma. Can be NULL.

Value

A vector of numeric, an estimation of H_0 at each t_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(), estimate_H0_list(), estimate_H0()

Examples

X <- generate_integrate_fractional_brownian(N = 1000, M = 300,
                                            H = 0.5, sigma = 0.01)
estimate_H0_deriv_list(X, t0_list = c(0.25, 0.5, 0.75), eps = 0.01, 
                       k0_list = c(8, 14, 8))

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