Perform an estimation of the bandwidth for the estimation of the covariance

Source: R/estimate_bandwidth.R

This function performs an estimation of the bandwidth to be used in the Nadaraya-Watson estimator.

estimate_bandwidths_covariance(
  curves,
  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_param

Vector (default = c(0.25, 0.5, 0.75)), the 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 points in the neighborhood to keep the curve in the estimation.

kernel_name

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

  • epanechnikov

  • uniform

  • biweight

Value

List, with elements:

  • sigma Estimation of the standard deviation of the noise

  • variance Estimation of the variance of the process

  • hursts Estimation of \(H_0\)

  • constants Estimation of \(L_0\)

  • bandwidths Estimation of the bandwidth

References

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