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- W2018142714 abstract "Quantization is a basic operation in communication, having aconsiderable impact also on control, in particular on control overcommunication networks, see cite{BROCKETT-QUANT} for an earlyreference. In this paper we consider a classic, seemingly innocentproblem of reconstructing a single signal value $theta^*$ whenmeasured with additive Gaussian noise, followed by uniformquantization of sensitivity $h$, with or without saturation. Apeculiar feature of the above estimation problem is that itsFisher information varies considerably with the noise variance andthe location of the true parameter. It is therefore a meaningfulobjective to adjust (shift) the quantization levels so as tomaximize the Fisher information or to inject additionalmeasurement noise for the same purpose. We shall focus on thefirst problem. Empirical evidence shows that, for given noisevariance, the Fisher information is maximal when the locationparameter is of the form $theta^*= kh + h/2$. Adjusting thequantization levels is equivalent, from the statistical point ofview, to adjusting, say increasing the location parameter by anamount of $delta>0$ to achieve a {it known} target, say$eta^*=kh + h/2$ for some integer $k$. The problem that weaddress in this paper is if such an adjustment of the problem canbe done adaptively, in the context of a previously developedrecursive, real-time estimation method for estimating $theta^*$,that was called a randomized $EM$-method for estimating$theta^*$. We give a positive answer to this question. Theproposed method results in considerable improvement in efficiency,supported both by the algebra of the asymptotic theory ofstochastic approximation, and by extensive experimental evidence.The basic ideas developed and presented for this benchmark problemcan be easily generalized for the multi-variable case." @default.
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- W2018142714 date "2008-01-01" @default.
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- W2018142714 title "Quantization with Adaptation - Estimation of Gaussian Linear Models" @default.
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- W2018142714 doi "https://doi.org/10.4310/cis.2008.v8.n3.a3" @default.
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