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A Non-Asymptotic Confidence Region with a Fixed Size for a Scalar Function Value: Applications in C-OTDR Monitoring Systems
JSK “EqualiZoom”, Astana, Kazakhstan
- 1 JSK “EqualiZoom”, Astana, Kazakhstan
Open Journal of Statistics·Volume 04 (2014)·Pages 578–585·Published 16 September 2014·DOI10.4236/ojs.2014.48054
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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.
KeywordsNon-Asymptotic Nonlinear EstimationSequential AnalysisConfidence RegionsGuaranteed AccuracyC-OTDR Monitoring System
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