Piecewise affine systems serve as an important approximation of nonlinear systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. Regressor parameters are then forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem w...

Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesi...

It is hard to overstate the importance of multidimensional scaling as an analysis technique in the broad sciences. Classical, or Torgerson multidimensional scaling is one of the main variants, with the advantage that it has a closed-form analytic solution. However, this solution is exact if and only if the distances are Euclidean. Conversely, there has been comparatively little discussion on wh...

System parameter identification is a necessary prerequisite for model-based control. In this paper, we propose an approach to estimate model parameters of robot servo actuators that does not require special testing equipment. We use Iterative Learning Control to determine the motor commands needed to follow a reference trajectory. To identify parameters, we fit a model for DC motors and frictio...

This paper reports a stable online adaptive identification technique for the identification of finite-dimensional dynamical models of dynamically positioned underwater robotic vehicles. Proofs for the identifier’s global stability, and for the input-tostate stability of this class of plants are reported. A direct comparison of the adaptive identification method to a conventional, offline, least...

In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. I...

The least-squares νth-order polynomial filtering and fixed-point smoothing problems of uncertainly observed signals are considered. The proposed estimators do not require the knowledge of the state-space model generating the signal, but only the moments (up to the 2νth one) of the signal and the observation noise, as well as the probability that the signal exists in the observations.

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict su$cient assumptions which however does not include important model structures such as, e.g. Box}Jenkins. Based on a simple least-squares appro...

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Different designs of experiments are compared according to the shape, concentration, etc. of the densities of the least-squares estimator (conditional densities, marginal densities). In contrast with D'Argenio (J. Pharmacokinetics Biopharmaceutics 9(16) (1981) 739-756), where marginal densities have been obtained by simulations, we present here a faster procedure based on well-elaborated approx...