presmoothing: Perform a pre-smoothing of the data.

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

Perform a pre-smoothing of the data.

Description

This function performs a pre-smoothing of the data using a Nadaraya-Watson estimator. We use an Epanechnikov kernel and a naive bandwidth.

Usage

presmoothing(
  curves,
  point = 0.5,
  delta_f = NULL,
  kernel = "epanechnikov",
  beta = 1,
  bandwidth_naive = 0
)

Arguments

curves	List, where each element represents a curve. Each curve have to be defined as a list with two entries: $t Sampling points $x Observed points
point	Numeric (default = 0.5), sampling point at which the data is pre-smoothed.
delta_f	Function (default = NULL), function to determine the delta.
kernel	String (default = 'epanechnikov'), the kernel used for the estimation: epanechnikov uniform biweight
beta	Numeric (default = 1), pre-specified regularity of the curves. The default value is 1, which correspond to at least one time differentiable curves.
bandwidth_naive	Numeric (default = 0), bandwidth to use for the presmoothing. If set to 0, the bandwidth will be defined as \frac{δ}{m}^{1 / (2β + 1)} where m is the mean number of sampling points per curve. δ is the length of the interval where the smoothing is done. β represents the regularity of the curves.

Value

List, with two entries:

• $grid Grid on which the smoothing has been done.

• $x_smooth The smoothed data.

References

S. Golovkine, N. Klutchnikoff and V. Patilea (2021) - Adaptive optimal estimation of irregular mean and covariance functions.

StevenGolovkine/funestim documentation built on June 15, 2022, 3:42 a.m.