estimate_L0: Perform an estimation of L_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 add ref.

Usage

estimate_L0(data, t0 = 0, H0 = 0, k0 = 2, sigma = NULL, density = FALSE)

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 H0. We will consider the 8k0 - 7 nearest points of t_0 for the estimation of H_0 when σ is unknown.
H0	Numeric, an estimation of H_0
k0	Numeric, the number of neighbors of t_0 to consider. Should be set as k0 = M * exp(-log(log(M))^2).
sigma	Numeric, true value of sigma. Can be NULL.
density	Logical, do the sampling points have a uniform distribution? (default is FALSE)

Value

Numeric, an estimation of L0.

See Also

Other estimate L_0: estimate_L0_list()

Examples

X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
estimate_L0(X, t0 = 0.5, H0 = 0.5, k0 = 2)

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