Parameter Estimation in the Presence of Bounded Data Uncertainties

Iterative solutions of min-max parameter estimation with bounded data uncertainties

This paper deals with the important problem of parameter estimation in the presence of bounded data uncertainties. Its recent closed-form solution in [1] leads to more meaningful results than alternative methods (e.g., total least-squares and robust estimation), when a priori bounds about the uncertainties are available. The derivation in [1] requires the computation of the SVD of the data matr...

Estimation of Bounded Model Uncertainties

We identify parameters of a given input-output model so that estimated model output is consistent with the measured output of the system modeled. Parameter estimation based on a set-membership approach is a nonprobabilistic method for characterizing the uncertainty with which each model parameter is known. The model is consistent with data if the estimated output domain contains measured system...

Estimation of Scale Parameter Under a Bounded Loss Function

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...

Data Fitting Problems with Bounded Uncertainties in the Data

A Fast Iterative Solution for Worst-case Parameter Estimation with Bounded Model Uncertainties

This paper deals with the problem of worst-case parameter estimation in the presence of bounded uncertainties in a linear regression model. The problem has been formulated and solved in [1,2]. It distinguishes itself from other estimation schemes, such as total-least-squares and H, methods, in that it explicitly incorporates an a-priori bound on the size of the Uncertainties. The closed-form so...