Robust estimation of the vector autoregressive model by a trimmed least squares procedure.

The vector autoregressive model is very popular for modeling multiple time series. Estimation of its parameters is done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and there is a need for robust alternatives. In this paper we propose to estimate the vector autoregressive model by using a trimmed least squares estimator. We show how the order of the autoregressive model can be determined in a robust way, and how confidence bounds around the robustly estimated impulse response functions can be constructed. The resistance of the estimators to outliers is studied on real and simulated data.Advantages; Calibration; Data; Estimator; Least-squares; M-estimators; Methods; Model; Optimal; Outliers; Partial least squares; Precision; Prediction; Regression; Research; Robust regression; Robustness; Squares; Variables; Yield; Robust estimation; Time; Time series; Order; Functions;

Model of Robust Regression with Parametric and Nonparametric Methods

In the present work, we evaluate the performance of the classical parametric estimation method "ordinary least squares" with the classical nonparametric estimation methods, some robust estimation methods and two suggested methods for conditions in which varying degrees and directions of outliers are presented in the observed data. The study addresses the problem via computer simulation methods. In order to cover the effects of various situations of outliers on the simple linear regression model, samples were classified into four cases (no outliers, outliers in the X-direction, outliers in the Y-direction and outliers in the XY-direction) and the percentages of outliers are varied between 10%, 20% and 30%. The performances of estimators are evaluated in respect to their mean squares error and relative mean squares error. Keywords: Simple Linear Regression model; Ordinary Least Squares Method; Nonparametric Regression; Robust Regression; Least Absolute Deviations Regression; M-Estimation Regression; Trimmed Least Squares Regression

Accuracy of MAP segmentation with hidden Potts and Markov mesh prior models via Path Constrained Viterbi Training, Iterated Conditional Modes and Graph Cut based algorithms

In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a solution of the MAP equation. The emission distribution is assumed the same in all models, and the difference lays in the Markovian prior hypothesis made over the labeling random field. The a priori labeling knowledge will be modeled with a) a second order anisotropic Markov Mesh and b) a classical isotropic Potts model. Under such models, we will consider three different segmentation procedures, 2D Path Constrained Viterbi training for the Hidden Markov Mesh, a Graph Cut based segmentation for the first order isotropic Potts model, and ICM (Iterated Conditional Modes) for the second order isotropic Potts model. We provide a unified view of all three methods, and investigate goodness of fit for classification, studying the influence of parameter estimation, computational gain, and extent of automation in the statistical measures Overall Accuracy, Relative Improvement and Kappa coefficient, allowing robust and accurate statistical analysis on synthetic and real-life experimental data coming from the field of Dental Diagnostic Radiography. All algorithms, using the learned parameters, generate good segmentations with little interaction when the images have a clear multimodal histogram. Suboptimal learning proves to be frail in the case of non-distinctive modes, which limits the complexity of usable models, and hence the achievable error rate as well. All Matlab code written is provided in a toolbox available for download from our website, following the Reproducible Research Paradigm

Model Order Selection in System Identification: New and Old Techniques

The thesis analyzes some techniques adopted for model order selection in system identification: both classical methods (cross-validation, information criteria, the F-test and the statistical tests on the residuals) and innovative ones are evaluated, such as PUMS criterion and kernel-based estimation. The theoretical description of these methods is accompanied by an experimental analysis. Two combinations of the methods are also introduced, proving that they allow a more robust order selectio

Robust Control Barrier Functions with Uncertainty Estimation

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure robust safety in the presence of model uncertainties, which may depend on control input and states. We present a new uncertainty/disturbance estimator with theoretical upper bounds on estimation error and estimated outputs, which are used to ensure robust safety by formulating a convex optimization problem using a high-order CBF. The possibly unsafe nominal feedback controller is augmented with the proposed estimator in two frameworks (1) an uncertainty compensator and (2) a robustifying reformulation of CBF constraint with respect to the estimator outputs. The former scheme ensures safety with performance improvement by adaptively rejecting the matched uncertainty. The second method uses uncertainty estimation to robustify higher-order CBFs for safety-critical control. The proposed methods are demonstrated in simulations of an uncertain adaptive cruise control problem and a multirotor obstacle avoidance situation

Estimating the accuracy of satellite ephemerides using the bootstrap method

International audienceContext: The accuracy of predicted orbital positions depends on the quality of the theorical model and of the observations used to fit the model. During the period of observations, this accuracy can be estimated through comparison with observations. Outside this period, the estimation remains difficult. Many methods have been developed for asteroid ephemerides in order to evaluate this accuracy. Aims: This paper introduces a new method to estimate the accuracy of predicted positions at any time, in particular outside the observation period. Methods: This new method is based upon a bootstrap resampling and allows this estimation with minimal assumptions. Results: The method was applied to two of the main Saturnian satellites, Mimas and Titan, and compared with other methods used previously for asteroids. The bootstrap resampling is a robust and practical method for estimating the accuracy of predicted positions

Reduced-order unscented Kalman filter in the frequency domain: Application to computational hemodynamics

Objective: The aim of this work is to assess the potential of the reduced order unscented Kalman filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. Methods: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameter after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. Results: First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. Conclusion: Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). Significance: The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data