estimate_bandwidth: Perform an estimation of the bandwidth

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

Description

This function performs an estimation of the bandwidth to be used in the Nadaraya-Watson estimator. The bandwidth is estimated using the method from add ref.

Usage

estimate_bandwidth(data, 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.
t0_list	A vector of numeric, the sampling points at which we estimate H0. We will consider the 8k0 - 7 nearest points of t_0 for the estimation of L_0 when σ is unknown.
k0_list	A vector of numeric, the number of neighbors of t_0 to consider. Should be set as k0 = (M / log(M) + 7) / 8 . 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, with elements:

• 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

Examples

X <- generate_fractional_brownian(N = 1000, M = 300,  H = 0.5, sigma = 0.05)
estimate_bandwidth(X)

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