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In this paper, a new class of hybrid lower bounds on the mean square-error of estimators is proposed. Derivation of the proposed class is performed by applying an integral transform on the centered likelihood-ratio (CLR) function. It is shown that the hybrid Cramer-Rao and Barankin bounds are the limits of convergent sequences of bounds, which are obtained from the proposed class using specific sequences...
It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramer-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin...
Confidence intervals for the maximum likelihood estimates (MLEs) are commonly used in statistical inference. To accurately construct such confidence intervals, one typically needs to know the distribution of the MLE. Standard statistical theory says normalized MLE is asymptotically normal with mean zero and variance being a function of the Fisher information matrix (FIM) at the unknown parameter....
Bayesian estimation of a threshold time (hereafter simply threshold) for the receipt of impulse signals is accomplished given the following: 1) data, consisting of the number of impulses received in a time interval from zero to one and the time of the largest time impulse; 2) a model, consisting of a uniform probability density of impulse time from zero to the threshold, and constituting the probability...
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