smooth_curves: Perform a non-parametric smoothing of a set of curves

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. The bandwidth is estimated using the method from add ref.

Usage

smooth_curves(data, U = NULL, t0_list = 0.5, k0_list = 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_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.
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_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
X_smooth <- smooth_curves(X)

X <- generate_piecewise_fractional_brownian(N = 1000, M = 300, 
                                            H = c(0.2, 0.5, 0.8), 
                                            sigma = 0.05)
X_smooth <- smooth_curves(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.