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On the minimax variance estimators of scale in time to failure models
이재원,Georgy L. Shevlyakov 대한수학회 2002 대한수학회보 Vol.39 No.1
A scale parameter is the principal parameterto be estimated, since it corresponds to oneof the main reliability characteristics, namely the average timeto failure. To provide robustness of scale estimators to grosserrors in the data, we apply the Huber minimax approach in time tofailure models of the statistical reliability theory. The minimaxvariance estimator of scale is obtained in the importantparticular case of the exponential distribution.
ON THE MINIMAX VARIANCE ESTIMATORS OF SCALE IN TIME TO FAILURE MODELS
Lee, Jae-Won,Shevlyakov, Georgy-L. Korean Mathematical Society 2002 대한수학회보 Vol.39 No.1
A scale parameter is the principal parameter to be estimated, since it corresponds to one of the main reliability characteristics, namely the average time to failure. To provide robustness of scale estimators to gross errors in the data, we apply the Huber minimax approach in time to failure models of the statistical reliability theory. The minimax valiance estimator of scale is obtained in the important particular case of the exponential distribution.
Song, Il Young,Shevlyakov, Georgy,Shin, Vladimir Hindawi Limited 2015 Mathematical problems in engineering Vol.2015 No.-
<P>This paper focuses on estimation of a nonlinear function of state vector (NFS) in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense) represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.</P>