Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimat...

This paper considers the estimation of dynamic models for panel data. It shows how to count and express the moment conditions implied by a variety of covariance restrictions. These conditions can be imposed in a GMM framework. Many of the moment conditions are nonlinear in the parameters. We derive a simple linearized estimator that is asymptotically as efficient as the nonlinear GMM estimator,...

We derive Monte Carlo-amenable solutions to the problem of unbiased estimation of a nonlinear function of the mean of a normal distribution. For most nonlinear functions the maximum likelihood estimator is biased. Our method yields a Monte Carlo approximation to the uniformly minimum variance unbiased estimator for a wide class of nonlinear functions. Applications to problems arising in the ana...

In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for...

A class of adaptive disturbance tracking controllers (ADTCs) is augmented with disturbance and state estimation and adaptive state feedback, in which a controller and estimator, which are designed on the basis of a lower-order model, are used to control a higher-order nonlinear plant. The ADTC requires that the plant be almost strict positive real (ASPR) to ensure stability. In this paper, we s...

This paper deals with the exact state sensitivity calculation required in the moving horizon estimator (MHE) for nonlinear networked control systems (NCS) presented in [4]. This NCS-MHE is capable of dealing with the network induced imperfections by formulating the estimation problem as a suitable optimization problem within a moving horizon framework. The resulting nonlinear program (NLP) can ...

In this paper, we investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-...

Estimation on a noisy signal observed by a nonlinear sensor taking the form of a threshold quantizer is considered. The optimal Bayesian estimator with minimal error is derived in this nonlinear setting. The existence of conditions where the performance of this estimator can be improved by raising the level of noise is established, both theoretically and numerically. These results constitute a ...

Abstract: A general class of discrete-time uncertain nonlinear stochastic systems with quadratic sum constraints is considered. A linear fixed order state estimator for state estimation is presented for various estimation error performance criteria in a unified framework. The observer is of order equal to the difference between the state and output vector dimensions. The performance criteria co...