R/smooth_curves.R
smooth_curves_regularity.RdThis function performs a non-parametric smoothing of a set of curves using the Nadaraya-Watson estimator when the regularity of the underlying curves is larger than 1. The bandwidth is estimated using the method from add ref. In the case of a regularly larger than 1, we currently assume that the regularly is the same all over the curve.
smooth_curves_regularity(data, U = NULL, t0 = 0.5, k0 = 2, K = "epanechnikov")
| data | A list, where each element represents a curve. Each curve have to be defined as a list with two entries:
|
|---|---|
| U | A vector of numerics, sampling points at which estimate the curves. If NULL, the sampling points for the estimation are the same than the observed ones. |
| t0 | Numeric, the sampling point at which we estimate \(H0\). We will consider the \(8k0 - 7\) nearest points of \(t_0\) for the estimation of \(H_0\) when \(\sigma\) is unknown. |
| k0 | Numeric, the number of neighbors of \(t_0\) to consider. Should be set as \(k0 = M * exp(-log(log(M))^2)\). |
| K | Character string, the kernel used for the estimation:
|
A list, which contains two elements. The first one is a list which contains the estimated parameters:
sigma An estimation of the standard deviation of the noise
H0 An estimation of \(H_0\)
L0 An estimation of \(L_0\)
b An estimation of the bandwidth
The second one is another list which contains the estimation of the curves:
$t The sampling points
$x The estimated points.
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