estimate_parameters_covariance: Perform a recursive estimation of the parameters over a grid...

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

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

Description

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.

Usage

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.

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