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In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment-based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi-maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μt of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk.

The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-a-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

This article presents an algebraic online parameters estimation method for linear time invariant LTI systems, subject to polynomial perturbations. Particular attention is given to practical implementation. The estimator may be expressed as a simple finite impluse response FIR filter, which is advantageous for online application, since the coefficients may be computed offline. The robustification against possible singularities is shown, the approach has the advantage to eliminate singularities that may occur in the experimental identification. This algorithm is illustrated experimentally on a permanent magnet stepper motor PMSM and a magnetic bearing for which parametric estimation is known to be a difficult task. The parameters to be estimated are sometimes measurable with difficulty and may vary slightly over time.

Summary In this paper, a repetitive learning control (RLC) scheme is developed for a class of nonlinear systems to handle an output tracking problem, where two state observers are introduced concurrently to estimate the unavailable control system and reference states information. The estimation of reference state information is because of the lack of reference internal model in the RLC design. By virtue of the periodicity of reference signals and the associated learning capability in control mechanism, the involved unstructured nonlinear uncertainties can be handled. The Lyapunov-like energy function method is adopted to facilitate the learning control design as well as property analysis thus achieve the asymptotical convergence of errors in state observation and output tracking simultaneously. Moreover, owing to the robustification of the learning controller that is addressed by incorporating projection, the proposed control scheme would be applicable in practice. In the end, an illustrative example is simulated to demonstrate the efficacy of the proposed RLC law. Copyright © 2014 John Wiley & Sons, Ltd.

Summary Instrumental variables estimators are designed to provide consistent parameter estimates for linear regression models when some covariates are correlated with the error term. We propose a new robust instrumental variables estimator (RIV) which is a natural robustification of the ordinary instrumental variables estimator (OIV). Specifically, we construct RIV using a robust multivariate location and scatter S-estimator to robustify the solution of the estimating equations that define OIV. RIV is computationally inexpensive and readily available for applications through the R-library riv. It has attractive robustness and asymptotic properties, including high resilience to outliers, bounded influence function, consistency under weak distributional assumptions, asymptotic normality under mild regularity conditions, and equivariance. We further endow RIV with an iterative algorithm which allows for the estimation of models with endogenous continuous covariates and exogenous dummy covariates. We study the performance of RIV when the data contains outliers using an extensive Monte Carlo simulation study and by applying it to a limited-access dataset from the Framingham Heart Study-Cohort to estimate the effect of long-term systolic blood pressure on left atrial size.

We give a description of the steps leading to a robustification of a dose–response study. The original experiment was designed and described by Rosenberger and Grill (1997) and has since been discussed by several other groups of researchers. Our robustification consists of redesigning the experiment so as to build in flexibility over a range of possible link functions, including the logistic link assumed by the original experimenters. We consider as well an asymptotic Neyman–Pearson test of the validity of the assumed link function.Copyright © 2011 John Wiley & Sons, Ltd.

The main role of high-throughput microarrays today is screening of relevant genes from a large pool of candidate genes. For prioritizing genes for subsequent studies, gene ranking based on the strength of the association with the phenotype is a relevant statistical output. In this article, we propose sample size calculations based on gene ranking and selection using the non-parametric Mann-Whitney-Wilcoxon statistic in microarray experiments. The use of the non-parametric statistic is expected to be advantageous in robustification in gene ranking for the deviation from normality and for possible scale change by using different platforms such as polymerase chain reaction-based platforms in subsequent studies in gene expression data. Application to the data set from a clinical study for lymphoma is given.

Partial least squares regression (PLS) is a linear regression technique developed to relate many regressors to one or several response variables. Robust methods are introduced to reduce or remove the effect of outlying data points. In this paper we show that if the sample covariance ma- trix is properly robustified further robustification of the linear regression steps of the PLS algorithm becomes unnecessary. The robust estimate of the covariance matrix is computed by searching for outliers in univariate projections of the data on a combination of random directions (Stahel- Donoho) and specific directions obtained by maximizing and minimizing the kurtosis coefficient of the projected data, as proposed by Pena and Prieto (2006). It is shown that this procedure is fast to apply and pro- vides better results than other procedures proposed in the literature. Its performance is illustrated by Monte Carlo and by an example, where the algorithm is able to show features of the data which were undetected by previous methods.

This paper presents the optimal regulator for a linear system with multiple time delays in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with multiple time delays in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.

Independent component analysis (ICA) is a statistical method for transforming multivariate data to components that are as independent of each other as possible. In recent years several algorithms were proposed that perform well in many situations. But when the data contain outliers, these methods may lead to wrong conclusions. Here we robustify the well-known FASTICA method by adding an outlier rejection rule which does not assume elliptical symmetry. This modification is supported by simulations and real data examples.

SUMMARY The concept of the integral sliding mode (ISM) is revised and applied for robustification of a linear time invariant min–max multi-model problem with uncertainties. Modified version of ISM ensures the insensitivity of the designed min–max control law with respect to matched uncertainty, starting from the beginning of the process, and guarantees that the unmatched part of uncertainties is minimized and not ’

This paper addresses the continuous-time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Kucera (Q) parameterization concept leads to a new development of observer-like controller structures. This method is combined with a nominal design of continuous-time generalized predictive control suitable for both minimum-phase and non-minimum-phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed-loop prototype characteristics with definite time-domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q-parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced-order) Q-parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase-lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences. Copyright © 2004 John Wiley & Sons, Ltd.

This paper proposes a novel approach to the problem of ℒ2 disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state-dependent scaling adapted to dynamic uncertainties and nonlinear-gain bounded uncertainties that do not necessarily have finite linear-gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ℋ∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial-state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state-dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd.

In this paper, we present two robust estimates for ARCH(p) models: τ - and filtered τ-estimates. These are defined by the minimization of conveniently robustified likelihood functions. The robustification is achieved by replacing the mean square error of the standardized observations with the square of a robust τ-scale estimate in the reduced form of the Gaussian likelihood function. The robust filtering procedure avoids the propagation of the effect of one outlier on subsequent conditional variances. A Monte-Carlo study shows that the maximum likelihood estimate practically collapses when there is only a small percentage of outlier contamination, while both robust estimates perform much better.

This paper presents a design for randomized clinical trials in which incomplete data are collected on the occurrence of potentially recurrent events through periodic monitoring. In particular, events are assumed to arise according to a point process, but information is available at the times of monitoring only if one or more events has occurred since the preceding monitoring point. The event process is modelled via a piecewise Poisson process, and a proportional rates model is introduced to represent the difference in event rates between treatment groups. The design was developed on the basis of a Wald-type test derived from the generalized estimating equations of Liang and Zeger (Biometrika 73, 13-22 (1986)). Robustification of the variance of the estimator of the treatment effect was considered under a random effects model with a semi-parametric mixture distribution. The design was adopted to address issues which arose in an osteoporosis trial conducted in Japan.

PLS regression methods have been used in applied fields for two decades. Techniques based on iteratively reweighted regression have appeared in the specialized literature with the contaminated data case. We propose a new robust PLS technique based on statistical procedures for covariance matrix robustification. We select the well-known Stahel–Donoho estimator (SDE). We include computational results comparing performance in terms of the standard PLS PRESS reduction if the robust PLS techniques are used. We use simulated and real data and include computational results showing the better robustness and efficiency for the new robust PLS method.Copyright © 1998 John Wiley & Sons, Ltd.

In classical linear regression model for analysis of medical data concerning hepatic extraction of insulin and c-peptide the fundamental assumption is that the subjects involved are of a similar nature. In reality, if this assumption is violated then the precision of the results is questionable. This paper suggests a robust alternative to overcome this problem. It is observed that the robustification may be a better option to determine an optimal quantity of insulin which minimizes the risk of damage associated with diabatic treatments.

This article studies calibration maintenance and transfer to build a statistical model that is able to predict analyte concentrations by a set of spectra. Noticing that the wavelength atoms are naturally ordered in a meaningful way, we propose a novel robust fused LASSO (RFL) based on high-dimensional sparsity techniques and a recent Θ-IPOD technique for robustification. This new approach can attain simultaneous wavelength selection and grouping as well as outlier identification, without any human intervention. An efficient and scalable algorithm is developed on the basis of the alternating direction method of multipliers. The obtained RFL model is sparse and shows improved prediction performance over the LASSO and ridge regression. Our results reveal that wavelengths can be combined into blocks, in a smart manner, to enhance the interpretability and reliability for super-resolution spectral analysis. Copyright © 2013 John Wiley & Sons, Ltd.

There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU-SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo-likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU-SILC survey. An ad-hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non-linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo-likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.

The paper offers an introductory survey of the area of robust estimation for applied statisticians, without demanding much mathematics. At first, the most important basic ideas of the robustness theory are explained using an example from the analysis of variance. Then the general reasons for and limits of the “robustification” of statistics are delineated. In particular, the various types of deviations from ideal models, such as gross errors, are discussed and their consequences are pointed out. The next part describes several simple robust estimators and their properties, ending with an outlook on robust estimators in linear models. As an appendix a number of frequent objections to and misunderstandings of robustness theory are discussed, refuted and clarified.