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This thesis if focused on the application of methods of robust econometrics to real economic data. We focuse on the issuies of international trade in Czech Republic and the problem of employment and growth of small businesses in Europe. We also focues on estimation of panel data by classical approaches (least squares, fixed effects, GMM) and bzy robust techniques. The first part of dissertation focuses on analyzing determinants of FDI in Czech manufacturing industry. The aim is to estimate a model where the stock of FDI is expressed as a function of several economic factors (K/L, profit per worker, R&D, Balassa index and others). We estimate these models by OLS, fixed effects and GMM. With regard to ambiguous results we used least trimmed squares as a diagnostic tool for detection of outliers. Elimination of two polluting industries out of the data set brings certain improvement in significance of some factors. The second part of dissertation we focus on an estimation of models of employment and net production in 28 European countries for small businesses as a function of economic and institutional variables by special technique of estimation. We describe robust version of within group fixed effects estimation. The aim of paper is to estimate a set of models and to test the properties of estimator. With...

International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirms the interest of this new and fast algorithm when the sample sizes are large. Finally, the ability of these recursive algorithms to deal with very high-dimensional data is illustrated on the robust estimation of television audience profiles conditional on the total time spent watching television over a period of 24 hours.

An S-estimator of regression is obtained by minimizing an M-estimator of scale applied to the residuals r_i. On the other hand, a generalized S-estimator (or GS-estimator) minimizes an M-estimator of scale based on all pairwise differences r_i - r_j. Generalized S-estimators have similar robustness properties as S-estimators, including a high breakdown point. In this paper we prove asymptotic normality for the GS-estimator of the regression parameters, as well as for the accompanying scale estimator defined by the minimal value of the objective function. It turns out that the asymptotic efficiency can be much higher than that of S-estimators. For instance, by using a biweight Ï -function we obtain a GS-estimator with 50% breakdown point and 68.4% efficiency. ispartof: Journal of Multivariate Analysis vol:51 issue:1 pages:148-177 status: published

In this paper a robust estimator against outliers along with some other existing interval estimators are considered for estimating the population standard devi ation. An extensive simulation study has been conducted to compare and evaluate the performance of th e interval estimators. The exact and the proposed robust method are easy to calculate and are n ot overly computer-intensive. It appears that the proposed robust method is performing bette r than other confidence intervals for estimating the population standard deviation, specificall y in the presence of outliers and/or data are from a skewed distribution. Some real-life examples are considered to illustrate the application of the proposed confidence intervals, which also supported t he simulation study to some extent

The paper quantifies the role of factors associated with the growth (or decline) of micro and small businesses in European economies. The growth is related to employment and value added in enterprises as well as to ten institutional variables. We test the data for consistency of behavioural patterns in various countries and gradually remove outlying observations, quite a unique a pproach in the panel data analysis, that can lead to erroneous conclusions when using the classical estimators. In the first part of this paper we outline a highly robust method of estimation based on fixed effects and least trimmed squares (LTS). In its second part we apply this method on the panel data of 28 countries in 2002-2008 testing for the hypothesis that micro and small businesses in Europe use different strategies for their growth. We run a series of econometric tests where we regress employment and total net production in micro and small businesses on three economic factors: gross capital returns, labour cost gaps in small relative to large enterprises and the GDP per capita. In addition, we also test the role of 10 institutional factors in the growth of familty businesses.

In this paper we propose accurate parameter and over-identification tests for indirect inference. Under the null hypothesis the new tests are asymptotically χ-super-2-distributed with a relative error of order n-super- - 1. They exhibit better finite sample accuracy than classical tests for indirect inference, which have the same asymptotic distribution but an absolute error of order n-super- - 1-2. Robust versions of the tests are also provided. We illustrate their accuracy in nonlinear regression, Poisson regression with overdispersion and diffusion models. Copyright 2010, Oxford University Press.

The paper is supported in part by the National Science Fund of Bulgaria, Grant No VU-MI -105/2005 and by ECO-NET 06 action 12634TJ founded by French Foreign Office., In the present paper we consider the branching process with immigration and its relationship to the Bienayme - Galton - Watson process with a random number of ancestors. Several estimators of the immigration component are considered - the conditional least squares estimator of Heyde - Seneta, the conditional weighted least squares estimator of Wei - Winnicki and the estimator of Dion and Yanev. Their comparison is based on simulations of the entire immigration family trees and computational results. The asymptotic normality of the estimator of Dion and Yanev is combined with the general idea of the trimmed and weighted maximum likelihood. As a result, robust modifications of the immigration component estimator is proposed. They are based on one and several realizations of the entire family tree and are studied via simulations and numerical results., 2000 Mathematics Subject Classi cation: 60J80.

Robust tahmin ediciler, veri kümesinde güvenli gözlemlerin homojen dağılmaması durumunda güvenli sonuçlar bulmak ve sapan değerlerin etkisini azaltmak amacıyla kullanılır. Tezin temel amacı; klasik regresyon analizinde sapan gözlemlerin varlığı nedeniyle standart varsayımların sağlanmaması durumunda en küçük kareler yöntemine alternatif olarak sunulan robust regresyon yöntemlerinin incelenmesidir. Bu çalı?mada önce sapan değerler, kırılma noktası ve etki fonksiyonu kavramları ele alınacak, sonra robust basit regresyon ve çoklu regresyondaki tahmin ediciler incelenecektir. Örneklerle bu tahmin ediciler, en küçük kareler tahmin edicisiyle kar?ıla?tırılacaktır. Anahtar kelimeler: En küçük kareler tahmin edici, En küçük medyan kareler tahmin edici, Kırılma noktası, Robust tahmin edici, Sapan değer Robust estimators are used for reducing the effects(weights) of outlying observations in the data set to get more reliable and stable estimators. The aim of this thesis is to propose robust regression procedures as an alternative method to Least Squares procedure which is widely used in classical regression analysis and very sensitive to outlying observations. In this thesis, firstly outlier and breaking point concepts will be introduced, secondly a general overview of estimators for robust simple and multiple regression will be given and finally these estimators will be compared with classical Least Squares estimators and examples will be provided. Keywords: Breaking Point, , Least median squares estimator, Least squares estimator, Outlier, Robust estimator, 120

17 pages, 7 figures, 1 table Most marine species are spatially clustered and thus the analysis of their distribution with geostatistical techniques is becoming increasingly common in fisheries studies, as a way of producing continuous distribution maps, reducing estimated error and analysing species spatial behaviour. The use of geostatistics is coupled with an increased computation power and development of statistical methods, leading to a greater availability of those to fisheries scientists. Thus, after the application of parametric classical geostatistical models to fisheries, a range of methods is now available that possibly are more adequate to fisheries data, typically non-normal, highly skewed and restricted to a low number of samples. However, the use of such recently available methods is still minimal and had not been widely applied or tested for its potential in fisheries studies. In the current work, we use simulated catch data, generated with an underlying spherical covariance function, considering two types of distribution function (Gaussian and log-Gaussian) and three levels of nugget variability (0, 30 and 50%). Twenty to 200 samples were randomly redrawn from the simulated data. Thus, for each case (sampling number, nugget and distribution) first, we test the efficiency of Mantel statistic in detecting significant autocorrelation. Second, we study the extent to which the originally defined covariance structure (variogram model parameters: nugget, sill and range) is recovered by different fitting methods: based on least squares (weighted least squares and Cressie) and on maximum likelihood (ML and relative ML) methods and the performance of the classical and robust variogram estimators. Third, we determine the reliability of several goodness-of-fit criteria (Akaike's, cross-validation, ‘gof’ and minimising function) in detecting the original model type (between spherical, exponential, Gaussian or linear). Finally, the bias of the fitting methods was modelled, so it can be corrected in future studies. Mantel test was able to detect significant autocorrelation in 20–85% of the cases, with Pearson r correlation coefficient varying between 0.04 and 0.12. The test statistic gave the best results with Gaussian data, increasing number of samples (more than 100) and decreasing nugget. Still, overall its behaviour was poor in identifying spatial autocorrelation. All fitting methods analysed gave significantly correct estimates for more than 50–70 samples, even when using log-Gaussian data with 50% nugget. Both estimator types behaved similarly in the Gaussian case, although the robust estimator performed considerably worse for log-Gaussian data. Using the least square methods, both weighted least squares (WLS) and Cressie behaved similarly well, for more than 50 samples, even with 50% nugget. As expected, the precision and accuracy of the estimates increased with the sample size, except for the range, which even when only 20 samples where used the estimates were correct. While the nugget was underestimated for any of the methods tested, the sill was generally overestimated, particularly in the presence of nugget. With increasing nugget variability (from 0 to 50%), more samples were required to accurately estimate the parameters. The range of variograms was in general overestimated by all methods studied. No goodness-of-fit criterion was able to detect the correct spatial model in more than 60% of the cases. Still, Akaike's, ‘gof’ using weights as pairs and the minimising function gave the best results. In this assessment, there was little influence of sample size and amount of nugget. A geostatistical analysis in a fisheries context is often carried out at the border of acceptability from a theoretical point of view; however, the results of this simulation study show that the reliability of a structural analysis can be improved when appropriate tools are employed This work was inserted on MMR Ph.D. program and it was financed by Fundação para a Ciência e a Tecnologia BD/21569/99 and VS Scholarship Programme of the German Federal Environmental Foundation (No. 20002/290)

Under the condition that the observations, which come from a high-dimensional population (X,Y), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg minaIE(r(a,Y)|X=x), where the loss function r(a,y) is measurable. Furthermore, some related simulations are illustrated by using the cross validation method for both bivariate linear and bivariate nonlinear time series contaminated by heavy-tailed errors. The M-estimator is applied to a series of S&P 500 index futures andspot prices to compare its performance in practice with the "usual" squared-loss regression estimator.

An overview of the track reconstruction algorithms used in the tracker of the CMS experiment at the LHC is presented. At the LHC, track reconstruction will be a very challenging task due to the high number of tracks foreseen. In addition to the standard Kalman filter, which serves as the basis for track reconstruction, several non-linear algorithms have been implemented.

Under the condition that the observations, which come from a high-dimensional population (X,Y), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg minaIE(r(a,Y) =x), where the loss function r(a,y) is measurable. Furthermore, some related simulations are illustrated by using the cross validation method for both bivariate linear and bivariate nonlinear time series contaminated by heavy-tailed errors. The M-estimator is applied to a series of S&P 500 index futures andspot prices to compare its performance in practice with the usual squared-loss regression estimator.

International audience; The aim of this study was to analyze somatic cell counts which is an indirect criterion. to assess susceptibility to mastitis. Data analyzed were weekly records (6448 somatic cell scores) out of 159 primiparous Holsteins and Holsteins x Normande cows raised at the INRA" Le Pin au Haras" experimental farm, France. Given the longitudinal structure of this data set, the analysis consists of modeling both the mean and the individual profiles. This was achieved via the use of mixed models including fixed effects for the average profiles and random effects for the adjusted individual profiles. As far as fixed effects are concerned, the main issue is to fit a time trend to the average profiles. For this, we employed the technique of fractional polynomials described in Royston and Altman (Appl. Stat. 43 (1994) 429-467) under several variance-covariance structures. The best second degree polynomial involved an intercept plus the time at the power (-1/3) (i.e., t-1/3) plus the latter times the logarithm of the time (i.e., t-1/3 × log (t)). Regarding random effects, model comparisons involved random coefficient models, exponential stationary stochastic processes and heterogeneous variances. The models that simultaneously included all these three structures turned out to be the best. For instance, random coefficient models did not fit the variance function well, even when the degree of the polynomial was high. This phenomenon partly justified the introduction of heteroskedastic models.; Analyse statistique des scores de cellules somatiques par la méthodologie des modèles mixtes appliquée à des données longitudinales. L'objectif de cette étude est d'analyser les comptages de cellules somatiques, qui constituent un critère indirect d'appréciation de la sensibilité aux mammites. Les données analysées étaient relatives à 6448 contrôles hebdomadaires de cellules somatiques du lait effectués sur 159 génisses de race Holstein et croisées Holstein x Normande, entretenues au domaine expérimental INRA-Le pin au Haras. Eu égard à la structure longitudinale des données, l'analyse a consisté à modéliser les profils moyens et individuels de réponse. À ce propos, ont été mis en œuvre des modèles mixtes dont les effets fixes décrivent les profils moyens et les effets aléatoires les profils individuels. Concernant les effets fixes, on a utilisé la technique des polynômes fractionnaires, décrite par Royston et Altman [29] assortie de différentes structures de variance-covariance. Le meilleur ajustement est fourni par un polynôme de second degré comportant un terme constant, le temps à la puissance moins un tiers (i.e., t-1/3) et ce même terme multiplié par le logarithme du temps (i.e., t-1/3 × log(t)). Concernant la partie aléatoire du modèle, les modèles mis en comparaison faisaient appel à une régression sur le temps à coefficients aléatoires, à des processus stochastiques stationnaires et à des variances hétérogènes. Ce sont les modèles qui incluaient simultanément ces trois structures qui se sont avérés les meilleurs. Ainsi, les modèles polynomiaux à degré élevé ne rendaient pas compte de l'évolution réelle de la variance avec le temps d'où le recours à des modèles hétéroscédastiques.

En la primera etapa de implementación de un sistema de control multivariado, usando la carta T ² de Hotelling con n observaciones históricas individuales, la presencia de outliers distorsiona la estimación de los parámetros del proceso y del límite de control debido al efecto de enmascaramiento. En este trabajo proponemos el uso de estimadores robustos para la construcción del estadístico T ² en esta primera etapa. Se prueba con estimadores MVE (elipsoide de mínimo volumen) y estimadores S biponderados, para el caso p = 2. Los resultados de simulaciones señalan que estos dos procedimientos resultan consistentes en la detección de outliers provenientes de perturbaciones en el vector de medias y de la matriz de varianzas covarianzas, consideradas individual y conjuntamente, con diferentes niveles de contaminación. In Phase I, Stage 1 of a multivariate process control, the implementation of a Hotelling's T ² chart with n individual observation, outliers cause difficulties with the estimation of process parameters and control limits due to masking effects. We propose procedures to construct robust estimators based upon the MVE (Minimum Volume Ellipsoide) and the biweighted S estimator, for case p = 2 (Bivariate Process). Simulation results show the good performance of these estimators before outliers presence, avoiding masking effects, when we are estimating the mean vector and varianza covarianza matrix, both individually and jointly. We make the investigation with different levels of contamination affecting the mean vector and varianza covarianza matrix.

In this paper we consider the channel representation based upon quadratic B-splines from a statistical point of view. Interpreting the channel representation as a kernel method for estimating probability density functions, we establish a channel algebra which allows to perform basic algebraic operations on measurements directly in the channel representation. Furthermore, as a central point, we identify the smoothing of channel values with a robust estimator, or equivalently, a diffusion process.

International audience

International audience; We propose a detection and classification system for various road situations, which is robust to light changes and different road markings. The road curves in an image are described with a Hough Transform, where histograms accumulate the contrast lines for each pixel. The resulting 2D histograms are used to train a Kohonen Neural Network. The final output classification can be used to improve road security, indicating dangerous situations to the driver or feeding a driving control system.

Electrophysiology measurements attempt to get information about neural pathological conditions by measuring electrical cortical responses to appopriate stimuli.

This article proposes a generalization and improvement on the method of Lenth (1989). The problem is solved by fixing outliers in highly contaminated samples. To do this a scale robust estimator is obtained and its performance is analyzed using computer simulations. The method is extremely simple to use and leads to the same results as the more complex one proposed by Box and Meyer (1986).

The National Agricultural Statistics Service (NASS) conducts quarterly multiple frame (MF) hog inventory surveys, using both a list and an area sampling frame. The MF survey direct expansion (DE) estimator for hogs is used as an indication by the National Board. A Robust Estimator (RE) is also currently being used by the National Board to augment the survey direct expansion total hog estimate. The first component of the RE is a DE non-outlier component. The second component of the RE is an average outlier component determined using data from several surveys. This report examines characteristics of those outlier records that are fundamental to computing the RE’s outlier component. Individual characteristics for outlier non-overlap (NOL) records for five states were studied. Three major causes of NOL outlier occurrence were found. They include increased expansion factors due to subsampling in follow-on surveys, the transitory and varying nature of hog production, and the location of hog operations on land with little or no agriculture. Individual list and NOL hog operation often produced more than one outlier within a frame-year. Results indicate that at the state level, some survey frame-year outlier totals and number of outliers occurring differ significantly. (The frame-year runs from June through May.) At the national level, no significant effects were found. Also, distributional differences for outliers were found between states. This is due in large part to the outlier cutoff values assigned each state. With no trends in outliers at the national level, the Robust Estimator should continue to be used without modification. However, the presence of a frame-year effect in outlier totals and outlier number of occurrences at the state level not only justifies the need for the RE but implies a modified RE might be investigated to help in making state level estimates. State level outlier cutoff values should be investigated in an attempt to locate optimum values for the RE’s ability to measure state and national board estimates.

A nonparametric minimum Hellinger distance estimator of location is introduced and shown to be asymptotically efficient at every symmetric density with finite Fisher information. Under small, possibly asymmetric, perturbations in such a density, the estimator is asymptotically robust in a technical sense which extends Hajek's concept of "regularity." A numerical example illustrates the computational feasibility of the estimator and its resistance to an arbitrary single outlier.

A rotationally invariant exponential model, which includes the Fisher-von Mises and Bingham distributions as special cases, is proposed for directional data in $R^p(p \geqslant 2)$. A new regression estimator for the model parameters is developed as a competitor to the maximum likelihood estimator. Both the new estimator and the MLE are asymptotically efficient at the postulated model and are robust under small departures from that model. Computationally, the regression estimator is much simpler since it requires no iterations or numerical integrations. Goodness-of-fit can be assessed by fitting nested special cases of the general model to the data.

Multi-baseline synthetic aperture radar (SAR) interferometric techniques, such as SAR tomography, is well established for 3-D reconstruction in the urban area. These methods usually require fairly large interferometric stacks (> 20 images) for a reliable reconstruction. Hence, they are usually not directly applicable for large-scale 3-D urban mapping using TanDEM-X data where only a few acquisitions are available in average for each city. This work proposes a new SAR tomographic processing framework to those extremely small stacks. The applicability of the algorithm is demonstrated using a TanDEM-X multi-baseline stack with five bistatic interferograms over the whole city of Munich, Germany. Systematic comparison of our result with TanDEM-X raw digital elevation models (DEM) and airborne LiDAR data shows that the relative height accuracy is two meters, which outperforms the TanDEM-X raw DEM. The promising performance of the proposed algorithm paved the first step towards high quality large-scale 3-D urban mapping.

The development of a track occupancy detector based on a combination of inertial and GNSS measurements

This paper proposes a robust controller / observer for anomaly estimation inside UAV networks. This method is based on both Lyapunov Krasovkii functional and dynamic behavior of TCP (Transmission Control Protocol). This observer considers, as a preliminary step, a statistical signature of the traffic exchanged in the network. Both observer and spectral signature provide an accurate estimation of the traffic which is used to detect and characterize the different anomalies that can be observed in the UAV network. Consequently, the different signatures that we can process, based on the different types of intrusion we generate in the network, are used to select the accurate model for robust control estimation. This selection is conducted by choosing a specific controller / observer among a dedicated bank of models. The first statistical signature extraction of the analyzed traffic is run with a multi-fractal analysis. This solution based on wavelet analysis has been selected because it offers a wide spectral characterization of the entire traffic process. The wavelet-based analysis methodology has been widely used for the last decade for Internet traffic characterization but this is the first time that this tool has been used on a UAV ad hoc network traffic. Moreover, several research studies on network anomaly estimation have been carried out using automatic control techniques. These studies provide methods for designing both observer and command laws dedicated to time delay problems while estimating the anomaly or intrusion in the system. As a first result, the designed controller / observer system has been successfully applied to some relevant practical problems such as ad hoc networks for aerial vehicles and the effectiveness is illustrated by using real traffic traces including Distributed Denial of Service (DDoS) attacks. Our first results show promising perspectives for Intrusion Detection System (IDS) in a fleet of UAVs. Indeed, different types of anomaly have been considered and they are all accurately detected by the intrusion detection process we propose in this paper.