A Non-Asymptotic Confidence Region with a Fixed Size for a Scalar Function Value: Applications in C-OTDR Monitoring Systems

Andrey V. Timofeev

JSK “EqualiZoom”, Astana, Kazakhstan.

DOI: 10.4236/ojs.2014.48054                

Abstract

In this paper we will investigate some non-asymptotic properties of the modified least squares estimates for the non-linear function f(λ*) by observations that nonlinearly depend on the parameter λ*. Non-asymptotic confidence regions with fixed sizes for the modified least squares estimate are used. The obtained confidence region is valid for a finite number of data points when the distributions of the observations are unknown. Asymptotically the suggested estimates represent usual estimates of the least squares. The paper presents the results of practical applications of the proposed method in C-OTDR monitoring systems.

Keywords

Non-Asymptotic Nonlinear Estimation, Sequential Analysis, Confidence Regions, Guaranteed Accuracy, C-OTDR Monitoring System

Conflicts of Interest

The authors declare no conflicts of interest.

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