estimate_L0_list: Perform the estimation of L_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 add ref.

Usage

estimate_L0_list(
  data,
  t0_list,
  H0_list,
  k0_list = 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_list	A vetor 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.
H0_list	A vector of numerics, an estimation of H_0 at every t_0 given in t0_list.
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).
sigma	Numeric, true value of sigma. Can be NULL.
density	Logical, do the sampling points have a uniform distribution? (default is FALSE)

Value

A vector of numerics, an estimation of L_0 at each t_0.

See Also

Other estimate L_0: estimate_L0()

Examples

X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
estimate_L0_list(X, t0_list = 0.5, H0_list = 0.5)

df_piece <- generate_piecewise_fractional_brownian(N = 1000, M = 300, 
                                                   H = c(0.2, 0.5, 0.8), 
                                                   sigma = 0.05)
estimate_L0_list(df_piece, t0_list = c(0.15, 0.5, 0.85), 
                 H0_list = c(0.2, 0.5, 0.8), k0 = 6)

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