Perform an estimation of the standard deviation of the noise.

Source: R/estimate_parameters.R

This function performs an estimation of the standard deviation of the noise in the curves. The following formula is used: $$\hat{\sigma^2} = \frac{1}{N}\sum_{n = 1}^{N} \frac{1}{2(M_n - 1)}\sum_{l = 2}^{M_n}(Y_{n, (l)} - Y_{n, (l-1)})^2$$

estimate_sigma(curves, delta = 0.1)

Arguments

curves

List, where each element represents a curve. Each curve have to be defined as list with two entries:

  • $t Sampling points.

  • $x Observed points.

delta

Numeric (default = 0.1), neighborhood for the estimation.

Value

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

References

S. Golovkine, N. Klutchnikoff, V. Patilea (2020) - Learning the smoothness of noisy curves with application to online curve estimation.