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

This function performs an estimation of the bandwidth for a univariate kernel regression estimator defined over continuous data.

estimate_bandwidth_covariance(
  curves,
  params,
  sigma = 0,
  grid_bandwidth = lseq(0.001, 0.1, length.out = 101),
  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 The sampling points

• $x The observed points.

params

List, estimation of the different parameters for the data points pair to estimate:

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

• $H Estimated regularity.

• $L Estimated constant.

• $var Estimated variance.

• $mom Estimated \(E(X^{2}_{t_0})\).

• $var_st Estimated \(E(X^{2}_{t_0})\).

sigma

Numeric, estimation of the std of the noise \(\sigma\).

grid_bandwidth

Vector (default = lseq(0.001, 0.1, length.out = 101)), grid of bandwidths.

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

Numeric, an estimation of the bandwidth.

References

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

See also

Other estimate bandwidth: estimate_bandwidth_mean()