This function performs a pre-smoothing of the data using a Nadaraya-Watson estimator. We use an Epanechnikov kernel and a naive bandwidth.
presmoothing(
curves,
point = 0.5,
delta_f = NULL,
kernel = "epanechnikov",
beta = 1,
bandwidth_naive = 0
)
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
Numeric (default = 0.5), sampling point at which the data is pre-smoothed.
Function (default = NULL), function to determine the delta.
String (default = 'epanechnikov'), the kernel used for the estimation:
epanechnikov
uniform
biweight
Numeric (default = 1), pre-specified regularity of the curves. The default value is 1, which correspond to at least one time differentiable curves.
Numeric (default = 0), bandwidth to use for the presmoothing. If set to 0, the bandwidth will be defined as δm1/(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.
List, with two entries:
$grid Grid on which the smoothing has been done.
$x_smooth The smoothed data.
S. Golovkine, N. Klutchnikoff and V. Patilea (2021) - Adaptive optimal estimation of irregular mean and covariance functions.