smooth_curves_regularity: Perform a non-parametric smoothing of a set of curves when...

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

Description

This function performs a non-parametric smoothing of a set of curves using the Nadaraya-Watson estimator when the regularity of the underlying curves is larger than 1. The bandwidth is estimated using the method from add ref. In the case of a regularly larger than 1, we currently assume that the regularly is the same all over the curve.

Usage

smooth_curves_regularity(data, U = NULL, t0 = 0.5, k0 = 2, K = "epanechnikov")

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.
U	A vector of numerics, sampling points at which estimate the curves. If NULL, the sampling points for the estimation are the same than the observed ones.
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.
k0	Numeric, the number of neighbors of t_0 to consider. Should be set as k0 = M * exp(-log(log(M))^2).
K	Character string, the kernel used for the estimation: epanechnikov (default) uniform beta

Value

A list, which contains two elements. The first one is a list which contains the estimated parameters:

• sigma An estimation of the standard deviation of the noise

• H0 An estimation of H_0

• L0 An estimation of L_0

• b An estimation of the bandwidth

The second one is another list which contains the estimation of the curves:

• $t The sampling points

• $x The estimated points.

Examples

X <- generate_integrate_fractional_brownian(N = 1000, M = 300, 
                                            H = 0.5, sigma = 0.01)
X_smooth <- smooth_curves_regularity(X, U = seq(0, 1, length.out = 101), 
                                     t0 = 0.5, k0 = 14)

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