Abstract: The practical efficient approach is suggested for
estimation of the seismoacoustic sources energy in C-OTDR
monitoring systems. This approach is represents the sequential plan
for confidence estimation both the seismoacoustic sources energy, as
well the absorption coefficient of the soil. The sequential plan
delivers the non-asymptotic guaranteed accuracy of obtained
estimates in the form of non-asymptotic confidence regions with
prescribed sizes. These confidence regions are valid for a finite
sample size when the distributions of the observations are unknown.
Thus, suggested estimates are non-asymptotic and nonparametric,
and also these estimates guarantee the prescribed estimation accuracy
in form of prior prescribed size of confidence regions, and prescribed
confidence coefficient value.
Abstract: Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.