Perform a non-parametric smoothing of a set of curves for covariance estimation.

Source: R/estimate_curve.R

This function performs a non-parametric smoothing of a set of curves using the Nadaraya-Watson estimator.

smooth_curves_covariance(
  curves,
  grid = seq(0, 1, length.out = 101),
  grid_param = c(0.25, 0.5, 0.75),
  grid_bandwidth = NULL,
  delta_f = NULL,
  n_obs_min = 2,
  kernel_name = "epanechnikov"
)

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.

grid

Vector (default = seq(0, 1, length.out = 101)), sampling points at which estimate the curves.

grid_param

Vector (default = c(0.25, 0.5, 0.75)), sampling points at which we estimate the parameters.

grid_bandwidth

Vector (default = NULL), grid of bandwidths.

delta_f

Function (default = NULL), function to determine the delta.

n_obs_min

Integer (default = 2), minimum number of observation for the smoothing.

kernel_name

String (default = 'epanechnikov'), the kernel used for the estimation:

  • epanechnikov

  • uniform

  • biweight

Value

A list, which contains three elements. The first one is a list which contains the estimated parameters:

  • sigma Estimation of the standard deviation of the noise.

  • variance Estimation of the variance of the process.

  • H0 Estimation of \(H_0\).

  • L0 Estimation of \(L_0\).

  • bandwidth Estimation of the bandwidth.

The second one is the bandwidths matrix. And the last one is the estimation of the covariance.

References

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