Perform a recursive estimation of the parameters over a grid of points for the estimation of the covariance.

Source: R/estimate_parameters.R

This function performs a recursive estimation of the different parameters used for the estimation of the covariance estimation of functional data. The recursion is made by small step onto the estimation of the regularity of the #' curves. The pre-smoothing of the data is done using a Nadaraya-Watson estimator and the used bandwidth modified using each new estimation of the regularity.

estimate_parameters_covariance(
  curves,
  grid = c(0.25, 0.5, 0.75),
  delta_f = NULL,
  kernel_name = "epanechnikov",
  beta = 1
)

Arguments

curves

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

grid

Vector (default = c(0.25, 0.5, 0.75)), sampling points at which the data is pre-smoothed.

delta_f

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

kernel_name

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

  • epanechnikov

  • uniform

  • biweight

beta

Numeric (default = 1), pre-specified regularity of the curves to start the recursion. The default value is 1, which correspond to at least one time differentiable curves.

Value

Dataframe, with columns:

  • $point Time point where the smoothing has been done.

  • $curves Smoothed curves.

  • $H Estimated regularity.

  • $L Estimated constant.

  • $var Estimated variance.

  • $mom Estimated \(E(X^{2}_{t_0})\)

  • $var_st \(Var(X_{s}X_{t)}\)

References

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