pflm.fpca.utils.get_measurement_error_variance#

get_measurement_error_variance(raw_cov: ndarray, reg_grid: ndarray, bandwidth: float, kernel_type: KernelType) → float[source][source]#

Estimate measurement error variance from raw covariance near the diagonal.

Smooths the raw covariance surface along the diagonal and leverages that the theoretical covariance at zero-lag equals the process variance, while the observed raw covariance includes measurement error. The difference (or an extrapolation to zero lag) yields an estimate of the noise variance.

Parameters:

raw_covnp.ndarray of shape (M, 5): Raw covariance entries (sid, t1, t2, w, cov).
reg_gridnp.ndarray of shape (nt,): Regular grid used to evaluate the smoothed covariance.
bandwidthfloat: Positive bandwidth for the smoothing kernel.
kernel_typeKernelType: Kernel used during smoothing.

Returns:

sigma2float: Estimated measurement error variance.

Raises:

ValueError: If inputs are inconsistent or bandwidth is invalid.