estimate_H0_list: Perform an estimation of H_0 given a list of t_0

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 using the method of Golovkine et al. (2020).

Usage

estimate_H0_list(data, t0_list, 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.
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_list(), estimate_H0_deriv(), estimate_H0()

Examples

X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
H0 <- estimate_H0_list(X, t0_list = 0.5, k0_list = 6)

X <- generate_piecewise_fractional_brownian(N = 1000, M = 300, 
                                            H = c(0.2, 0.5, 0.8), 
                                            sigma = 0.05)
H0 <- estimate_H0_list(X, t0_list = c(0.15, 0.5, 0.85), k0_list = c(2, 4, 6))
H0 <- estimate_H0_list(X, t0_list = c(0.15, 0.5, 0.85), k0_list = 6)

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