On Parameter Estimation of Hidden Telegraph Process
Rafail Khasminskii, Yury Kutoyants
TL;DR
This paper develops an asymptotically efficient method for estimating parameters of a two-state telegraph process observed with Gaussian noise, combining method of moments and one-step MLE techniques.
Contribution
It introduces a novel estimation procedure that achieves asymptotic normality and efficiency for the hidden telegraph process parameters.
Findings
Method of moments estimator described for large samples
One-step MLE process constructed for efficient parameter estimation
Estimator achieves asymptotic normality and efficiency
Abstract
The problem of parameter estimation by the observations of the two-state telegraph process in the presence of white Gaussian noise is considered. The properties of estimator of the method of moments are described in the asymptotics of large samples. Then this estimator is used as preliminary one to construct the one-step MLE-process, which provides the asymptotically normal and asymptotically efficient estimation of the unknown parameters.
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