This paper addresses two issues concerning the separate-bias Kalman estimator. The first of these issues deals with the derivation of the optimal estimator for the general case in which the bias vector is stochastic in nature, and the second issue deals with defining a suitable suboptimal realization of the generalized estimator.

In this paper, we establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator.

Security of Cyber-Physical Systems (CPS) has gained increasing attention in recent years. Most existing works mainly investigate the system performance given some attacking patterns. In this paper, we investigate how an attacker should schedule its Denial-of-Service (DoS) attacks to degrade the system performance. Specifically, we consider the scenario where a sensor sends its data to a remote ...

We propose an optimal quadtree (QT)-based motion estimator for video compression. It is optimal in the sense that for a given bit budget for encoding the displacement vector field (DVF) and the QT segmentation, the scheme finds a DVF and a QT segmentation which minimizes the energy of the resulting displaced frame difference (DFD). We find the optimal QT decomposition and the optimal DVF jointl...

We propose an estimator for the α fractional derivative of a distribution function. Our estimator, based on finite differences of the empirical df generalizes the estimator proposed by Maltz (1974) for the nonnegative real case. The asymptotic bias, variance and the consistency of the estimator are studied. Finally, the optimal choice for the ”smoothing parameter” proves that even in the fracti...

This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It ...

We give a comprehensive theoretical characterization of a nonparametric estimator for the L2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is √ n-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence int...

An optimal multistage Kalman estimator (OMSKE) is proposed as a generalization of the optimal two-stage Kalman estimator for the reduction of the computational burden of the Kalman estimator (KE) for discrete-time linear time-varying systems with triangular transition matrices. This new filter is obtained by applying a multistage transformation to decouple the covariances of the KE. It is shown...

This paper presents a density estimator based upon a histogram computed on a fuzzy partition. We prove the consistency of this estimator in the Mean Squared Error (MSE). We give the optimal bin width of the estimator which minimizes the Asymptotic Integrated Mean Squared Error (AIMSE). c © 2008 Elsevier B.V. All rights reserved.

We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introd...