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ON ROBUST MINIMAX APPROACH UNDER FINITE DISTRIBUTIONS
Shevlyakov, Georgiy L.,Lee, Jae-Won,Park, Sung-Wook Korean Mathematical Society 1998 대한수학회논문집 Vol.13 No.3
As most of distributions appearing in applications are finite but with the unknown domain of finiteness, we propose to use the robust minimax approach for the determination of the boundaries of this domain. The obtained least favorable distribution minimizing Fisher information over the class of the approximately Gaussian finite distributions gives the reasonable sizes of the domain of finiteness and the thresholds of truncation.
Shevlyakov, G.,Kiseon Kim IEEE 2006 IEEE transactions on information theory Vol.52 No.3
<P>In practical communication environments, it is frequently observed that the underlying noise distribution is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To describe partially known noise distribution densities, a distribution class characterized by the upper-bounds upon a noise variance and a density dispersion in the central part is used. The results on the minimax variance estimation in the Huber sense are applied to the problem of asymptotically minimax detection of a weak signal. The least favorable density minimizing Fisher information over this class is called the Weber-Hermite density and it has the Gaussian and Laplace densities as limiting cases. The subsequent minimax detector has the following form: i) with relatively small variances, it is the minimum L<SUB>2</SUB>-norm distance rule; ii) with relatively large variances, it is the L<SUB>1 </SUB>-norm distance rule; iii) it is a compromise between these extremes with relatively moderate variances. It is shown that the proposed minimax detector is robust and close to Huber's for heavy-tailed distributions and more efficient than Huber's for short-tailed ones both in asymptotics and on finite samples</P>
Robust Distributed Detection with Total Power Constraint in Large Wireless Sensor Networks
Jintae Park,Shevlyakov, G.,Kiseon Kim IEEE 2011 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Vol.10 No.7
<P>In practical problems of signal detection, it is quite common that the underlying noise distribution is not Gaussian and may vary in a wide range from light- to heavy-tailed forms. To design a robust fusion rule for distributed detection in wireless sensor networks, an asymptotic maximin approach is used by introducing weak signals in the canonical parallel fusion model. Explicit formulas for the detection and false alarm probabilities are derived. The analytic results are written out for the classes of nondegenerate, with a bounded variance and contaminated Gaussian noise distributions. Numerical and simulation results are obtained to justify robustness and asymptotic characteristics of the proposed fusion rule.</P>
Distributed Detection and Fusion of Weak Signals in Fading Channels with Non-Gaussian Noises
Jintae Park,Shevlyakov, G.,Kiseon Kim IEEE 2012 IEEE COMMUNICATIONS LETTERS Vol.16 No.2
<P>Distributed detection and information fusion have received recent research interest due to the success of emerging wireless sensor network (WSN) technologies. For the problem of distributed detection in WSNs under energy constraints, a weak signal model in the canonical parallel fusion scheme with additive non-Gaussian noises and fading channels is considered. To solve this problem in the Neyman-Pearson setting, a unified asymptotic fusion rule generalizing the maximum ratio combiner (MRC) fusion rule is proposed. Explicit formulas for the threshold and detection probability applicable for wide classes of fading channels and noise distributions are written out. Both asymptotic analysis and Monte Carlo modeling are used to examine the performance of the proposed detection fusion rule.</P>
Maximin Distributed Detection in the Presence of Impulsive Alpha-Stable Noise
Jintae Park,Shevlyakov, G.,Kiseon Kim IEEE 2011 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS Vol.10 No.6
<P>The distributed detection problem in wireless sensor networks is studied under the impulsive α-stable noise assumption. Since symmetric α-stable density does not have a closed form, its approximation, the bi-parameter Cauchy Gaussian mixture model, is used to describe the impulsive behavior of α-stable noises. With this model, we propose a low-complexity robust fusion rule by taking the maximin setting with respect to the detection probability. An explicit formula for the detection probability is derived. Robustness of the proposed maximin fusion rule is justified by numerical and simulation results for α-stable noises.</P>
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.
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>
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.