PDF HAMPEL CONTRIBUTIONS TO THE THEORY OF ROBUST ESTIMATION



Pdf Hampel Contributions To The Theory Of Robust Estimation

Package ‘RobLox’ The Comprehensive R Archive Network. For detection of gross errors in processing triangulation networks, this paper introduces the principle of designing robust estimators with high breakdown points based on the median approach. Three examples presented in the paper show how to form the combinations of observations while considering, Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the clear benefits of efficient loss functions..

Robust estimators for simultaneous equations models

Robust inference in sample selection models. Package ‘ROptEstOld’ August 3, 2018 Version 1.1.0 Date 2018-08-01 Title Optimally Robust Estimation - Old Version Description Optimally robust estimation using S4 classes and methods., a robust measure of spread is employed in preference to the standard deviation of the residuals. For example, For example, a common approach is to take σ = MAR/0.6745, where MAR is the median absolute residual..

of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or The contributions to biased-robust estimation follow naturally and will be discussed in detail concerning both the estimation approaches and the Monte Carlo simulation comparisons. Robust Estimation The problem of robustness in statistics goes back to the beginnings of statistics, especially in terms of measures of location. In fact, Rey (1983) notes that the Greek besiegers of antiquity

In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such ROBUST MULTIVARIATE ANALYSIS Download Robust Multivariate Analysis ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to ROBUST MULTIVARIATE ANALYSIS book pdf for free now.

The contributions to biased-robust estimation follow naturally and will be discussed in detail concerning both the estimation approaches and the Monte Carlo simulation comparisons. Robust Estimation The problem of robustness in statistics goes back to the beginnings of statistics, especially in terms of measures of location. In fact, Rey (1983) notes that the Greek besiegers of antiquity Iterative Procedure Robust Estimation Asymptotic Normality Robust Regression Robustness Property These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of … theory on M-estimation. M-estimators share many of the convenient proper- M-estimators share many of the convenient proper- ties of least-squares estimators, and at the same time are much more robust

3 robust estimation methods In the second half of the last century unconventional estimation methods were developed in the theory of linear programming in addition to the standard estimation methods. The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down, that is, to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the finite sample as well as the asymptotic breakdown

Crash course in robust mean estimation. up vote 13 down vote favorite. 11. I have a bunch (around 1000) of estimates and they are all supposed to be estimates of long-run elasticity. A little more than half of these is estimated using method A and the rest using a method B. Somewhere I read something like "I think method B estimates something very different than method A, because the estimates ROBUST MULTIVARIATE ANALYSIS Download Robust Multivariate Analysis ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to ROBUST MULTIVARIATE ANALYSIS book pdf for free now.

Iterative Procedure Robust Estimation Asymptotic Normality Robust Regression Robustness Property These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. sense, robust statistics is a body of knowledge, partly formalized into ‘theories of robustness,’ relating to deviations from idealized assumptions in statistics.” 1.2.

Package ‘RobLox’ The Comprehensive R Archive Network

pdf hampel contributions to the theory of robust estimation

Frank Hampel The Mathematics Genealogy Project. In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable ., Introducing concepts, theory, and applications, Robust Statistics is accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. The text covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. It also treats the change-of.

SURVIVAL ANALYSIS FROM THE VIEWPOINT OF HAMPEL'S

pdf hampel contributions to the theory of robust estimation

outliers Crash course in robust mean estimation - Cross. A Theory of Robust Long-Run Variance Estimation Ulrich K. M¨uller∗ Princeton University Economics Department Princeton, NJ, 08544 Abstract Long-run variance estimation can typically be viewed as the problem of estimat- Some Contributions to Robust Inference for Discrete explicitly treated robust estimation for discrete data, although in prin-cip1e existing techniques can be used. One technique is to modify the maximum likelihood estimator in the following way. Replace the likelihood score in the estimating equation by a suitable bounded score functionljJ to limit the effect that an indivi-dual.

pdf hampel contributions to the theory of robust estimation


Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are … Outlier Detection and Robust Estimation in Nonparametric Regression (2011) in the context of linear models, however, the extension from linear model to nonparametric mod-

Efficient and Robust Fitting of Lognormal Distributions Robert Serfling1 UniversityofTexasatDallas May2002 1Department of Mathematical Sciences, University of … While Huber’s minimax theory is one of the key ideas in robust statistics and leads to elegant and exact flnite sample results, it seems di–cult to extend it to general parametric models, when no invariance structure is available.

theory on M-estimation. M-estimators share many of the convenient proper- M-estimators share many of the convenient proper- ties of least-squares estimators, and at the same time are much more robust In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such

Iterative Procedure Robust Estimation Asymptotic Normality Robust Regression Robustness Property These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such

of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location , scale , and regression parameters .

Robust estimators for simultaneous equations models Krishnakumar, J.; Ronchetti, E. 1997-06-01 00:00:00 This paper presents a class of robust estimators for linear and non-linear simultaneous equations models, which are a direct generalization of the maximum likelihood estimator. The new estimators are obtained as solutions of a generalized likelihood equation. They are resistant to … In the last decades, robust estimation has been widely applied to overcome the presence of gross errors in observations. Recently it has been shown that robust estimation, if computed appropriately, is able to cope with a larger amount of gross errors and also capable of providing reliable estimations in situations where systematic errors are present. It is the purpose of this paper to propose

of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or ROBETH (written in ANSI FORTRAN 77) is a systematized collection of algorithms that allows computation of a broad class of procedures based on M- and high-breakdown point estimation, including robust regression, robust testing of linear hypotheses, and robust coveriances.

90 Devlin, S.J., Gnanadesikan, R. and Kettenring, J.R., Robust estimation and outlier detection with correlation coefficients, Biometrika, 62 of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or

pdf hampel contributions to the theory of robust estimation

estimation methods and Bayesian robust approaches.1 On the basis of return-risk tradeoff, we address two aspects of portfolio selection prob- lem: 1) what is a proper risk measure that can adapt to the vicissitudes of the financial market MAIN CONTRIBUTIONS OF ROBUST STATISTICS TO MODERN STATISTICS Here is a list of main ideas, concepts, and tools which robust statistics contributed to modern statistics. We focus only on those basic ideas which were developed in robust statistics but which are nowadays general tools in modern statistics. a) Models are only approximations to reality Of course, this is a standard …

Robust Shrinkage Range Estimation Algorithms Based on

pdf hampel contributions to the theory of robust estimation

Package ‘ROptEstOld’ The Comprehensive R Archive Network. The contributions to biased-robust estimation follow naturally and will be discussed in detail concerning both the estimation approaches and the Monte Carlo simulation comparisons. Robust Estimation The problem of robustness in statistics goes back to the beginnings of statistics, especially in terms of measures of location. In fact, Rey (1983) notes that the Greek besiegers of antiquity, sense, robust statistics is a body of knowledge, partly formalized into ‘theories of robustness,’ relating to deviations from idealized assumptions in statistics.” 1.2..

On the design of estimators with high breakdown points for

On the design of estimators with high breakdown points for. The theory of robust statistics deals with deviations from the assumptions on the model and is concerned with the construction of statistical procedures which are still reliable and reasonably efficient in a neighborhood of the model; see the books by Huber (1981), Hampel,, Herein, we present robust shrinkage range estimation algorithms for which received signal strength measurements are used to estimate the distance between emitter and sensor. The concepts of robustness for the Hampel filter and skipped filter are combined with shrinkage for the positive blind minimax and Bayes shrinkage estimation. It is.

proficiency testing data on analysis of lead in aqueous solution Sushree approaches viz. Cochran’s test, Grubb’s test, Hampel’s test, classical z-score, median and NIQR method, robust statistical analysis : Algorithm A (ISO 13528) and NATA method. The robust estimate of average and uncertainty values derived from ISO 13528 method are very close to the reference value for the 1 and 2 ROBETH (written in ANSI FORTRAN 77) is a systematized collection of algorithms that allows computation of a broad class of procedures based on M- and high-breakdown point estimation, including robust regression, robust testing of linear hypotheses, and robust coveriances.

The estimation technique, which is based on optimal B-robust estimates, will assign weights to each observation and give estimates of the parameters based on the data which are well modeled by the distribution. Thus, observations which are not consistent with the proposed distribution can be identified and the validity of the model can be assessed. The method is illustrated on Venice sea level Package ‘RobLox’ August 3, 2018 Version 1.1.0 Date 2018-08-01 Title Optimally Robust Influence Curves and Estimators for Location and Scale Description Functions for the determination of optimally robust influence curves and

Title: Contributions to the theory of robust inference: Creator: Salibian-Barrera, Matias: Date Issued: 2000: Description: We study the problem of performing statistical inference based on robust estimates when the distribution of the data is only assumed to belong to a contamination neighbourhood of a known central distribution. Stochastic Process Probability Theory Mathematical Biology Robust Estimation Asymptotic Variance These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

expanded upon his earlier results, and by 1972 the world of robust estimation was considerably larger, with optimality results now for three classes of estimates – R estimates and L estimates joining Huber’s 1964 M estimates. Iterative Procedure Robust Estimation Asymptotic Normality Robust Regression Robustness Property These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Some Contributions to Robust Inference for Discrete explicitly treated robust estimation for discrete data, although in prin-cip1e existing techniques can be used. One technique is to modify the maximum likelihood estimator in the following way. Replace the likelihood score in the estimating equation by a suitable bounded score functionljJ to limit the effect that an indivi-dual Abstract. The notion of breakdown point was introduced by Hampel (1968, 1971) and has since played an important role in the theory and practice of robust statistics.

Crash course in robust mean estimation. up vote 13 down vote favorite. 11. I have a bunch (around 1000) of estimates and they are all supposed to be estimates of long-run elasticity. A little more than half of these is estimated using method A and the rest using a method B. Somewhere I read something like "I think method B estimates something very different than method A, because the estimates SURVIVAL ANALYSIS FROM THE VIEWPOINT OF HAMPEL'S THEORY FOR ROBUST ESTIMATION by Steven J. Samuels '.. Department of Biostatistics University of North Carolina at Chapel Hill

The theory of robust statistics deals with deviations from the assumptions on the model and is concerned with the construction of statistical procedures which are still reliable and reasonably efficient in a neighborhood of the model; see the books by Huber (1981), Hampel, of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or

Outlier Detection and Robust Estimation in Nonparametric Regression (2011) in the context of linear models, however, the extension from linear model to nonparametric mod- Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the clear benefits of efficient loss functions.

In the last decades, robust estimation has been widely applied to overcome the presence of gross errors in observations. Recently it has been shown that robust estimation, if computed appropriately, is able to cope with a larger amount of gross errors and also capable of providing reliable estimations in situations where systematic errors are present. It is the purpose of this paper to propose Robust Statistics for Multivariate Methods. 3. data (which include missing data), the correlation between ML1TOT and ML2TOT was found to be 0.84 (robust estimation), whereas it is equal to 0.20

In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable . In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable .

The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down, that is, to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the finite sample as well as the asymptotic breakdown The goal of this PhD Thesis is the definition of new robust estimators, thereby extending the available theory and exploring new directions for applications in finance. The Thesis contains three papers, which analyze three different types of estimators: M-, Minimum Distance- and R- estimators. The

“For contributions to robust and optimal control theory.” 2018- JOHN TSITSIKLIS Clarence J. Lebel Professor of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA “For contributions to the theory and application of optimization in large dynamic and distributed systems.” 2017- RICHARD M. MURRAY Everhart Professor of Control & Dynamical Systems ROBUST MULTIVARIATE ANALYSIS Download Robust Multivariate Analysis ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to ROBUST MULTIVARIATE ANALYSIS book pdf for free now.

In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable . Space-Efficient Estimation of Robust Statistics and Distribution Testing tation, almost all of the literature on the algorithmic theory of data-streams considers only “empirical problems”,where the goal is to compute a function of the data present in the stream rather than to infer somethingabout the source of the stream. Our contributions are two-fold. First, we provide results

While Huber’s minimax theory is one of the key ideas in robust statistics and leads to elegant and exact flnite sample results, it seems di–cult to extend it to general parametric models, when no invariance structure is available. a robust measure of spread is employed in preference to the standard deviation of the residuals. For example, For example, a common approach is to take σ = MAR/0.6745, where MAR is the median absolute residual.

ROBUST MULTIVARIATE ANALYSIS Download Robust Multivariate Analysis ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to ROBUST MULTIVARIATE ANALYSIS book pdf for free now. 3 robust estimation methods In the second half of the last century unconventional estimation methods were developed in the theory of linear programming in addition to the standard estimation methods.

Frank Hampel The Mathematics Genealogy Project

pdf hampel contributions to the theory of robust estimation

Efficient and Robust Fitting of Lognormal Distributions. theory on M-estimation. M-estimators share many of the convenient proper- M-estimators share many of the convenient proper- ties of least-squares estimators, and at the same time are much more robust, Introducing concepts, theory, and applications, Robust Statistics is accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. The text covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. It also treats the change-of.

Space-Efficient Estimation of Robust Statistics and

pdf hampel contributions to the theory of robust estimation

A new infinitesimal approach to robust estimation. Learning (RSL) for linear models within a continuous optimization framework based on robust M-estimation. The framework applies to a variety of linear learning problems in computer vision including eigen-analysis and structure from motion. Several synthetic and natural examples are used to develop and illustrate the theory and applications of robust subspace learning in computer vision of J. W. Tukey , P. J. Huber or F. R. Hampel. Some of the most used robust Some of the most used robust regression estimators are M-Estimators, Least Trimmed Squares (LTS) or.

pdf hampel contributions to the theory of robust estimation


Stochastic Process Probability Theory Mathematical Biology Robust Estimation Asymptotic Variance These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. Qualitative robustness, influence function, and breakdown point are three main concepts to judge an estimator from the viewpoint of robust estimation.

ROBETH (written in ANSI FORTRAN 77) is a systematized collection of algorithms that allows computation of a broad class of procedures based on M- and high-breakdown point estimation, including robust regression, robust testing of linear hypotheses, and robust coveriances. The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down, that is, to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the finite sample as well as the asymptotic breakdown

ROBETH (written in ANSI FORTRAN 77) is a systematized collection of algorithms that allows computation of a broad class of procedures based on M- and high-breakdown point estimation, including robust regression, robust testing of linear hypotheses, and robust coveriances. 90 Devlin, S.J., Gnanadesikan, R. and Kettenring, J.R., Robust estimation and outlier detection with correlation coefficients, Biometrika, 62

Robust estimators for simultaneous equations models Krishnakumar, J.; Ronchetti, E. 1997-06-01 00:00:00 This paper presents a class of robust estimators for linear and non-linear simultaneous equations models, which are a direct generalization of the maximum likelihood estimator. The new estimators are obtained as solutions of a generalized likelihood equation. They are resistant to … This paper treats essentially the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties. A theory of robust estimation “near” strict parametric models is briefly sketched and applied to some classical situations. Relations

Frank Hampel's use of the influence curve in robust estimation is a central concept, but one beyond the scope of this article. Hence the reader interested in influence curves is referred to Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are …

Package ‘RobLox’ August 3, 2018 Version 1.1.0 Date 2018-08-01 Title Optimally Robust Influence Curves and Estimators for Location and Scale Description Functions for the determination of optimally robust influence curves and In Section A the theory of convergence is studied as a prelude to validating the use of the particular M-estimators... [Show more] given in Section B and C. Section B initially covers the view of robustness of Hampel (1968) but places more emphasis on the application of the notions of differentiability of functionals and on M-estimators of a general parameter that are robust against "tail

The goal of this PhD Thesis is the definition of new robust estimators, thereby extending the available theory and exploring new directions for applications in finance. The Thesis contains three papers, which analyze three different types of estimators: M-, Minimum Distance- and R- estimators. The Herein, we present robust shrinkage range estimation algorithms for which received signal strength measurements are used to estimate the distance between emitter and sensor. The concepts of robustness for the Hampel filter and skipped filter are combined with shrinkage for the positive blind minimax and Bayes shrinkage estimation. It is

90 Devlin, S.J., Gnanadesikan, R. and Kettenring, J.R., Robust estimation and outlier detection with correlation coefficients, Biometrika, 62 For detection of gross errors in processing triangulation networks, this paper introduces the principle of designing robust estimators with high breakdown points based on the median approach. Three examples presented in the paper show how to form the combinations of observations while considering

Frank Hampel's use of the influence curve in robust estimation is a central concept, but one beyond the scope of this article. Hence the reader interested in influence curves is referred to 90 Devlin, S.J., Gnanadesikan, R. and Kettenring, J.R., Robust estimation and outlier detection with correlation coefficients, Biometrika, 62

a robust measure of spread is employed in preference to the standard deviation of the residuals. For example, For example, a common approach is to take σ = MAR/0.6745, where MAR is the median absolute residual. Qualitative robustness, influence function, and breakdown point are three main concepts to judge an estimator from the viewpoint of robust estimation.

sense, robust statistics is a body of knowledge, partly formalized into ‘theories of robustness,’ relating to deviations from idealized assumptions in statistics.” 1.2. The optimal choise for s n is an M-estimate of scale applied to the residuals about the median. The optimal choice for the score function ψ is a truncated and rescaled maximum likelihood score function for the central model.

MAIN CONTRIBUTIONS OF ROBUST STATISTICS TO MODERN STATISTICS Here is a list of main ideas, concepts, and tools which robust statistics contributed to modern statistics. We focus only on those basic ideas which were developed in robust statistics but which are nowadays general tools in modern statistics. a) Models are only approximations to reality Of course, this is a standard … estimation methods and Bayesian robust approaches.1 On the basis of return-risk tradeoff, we address two aspects of portfolio selection prob- lem: 1) what is a proper risk measure that can adapt to the vicissitudes of the financial market

Herein, we present robust shrinkage range estimation algorithms for which received signal strength measurements are used to estimate the distance between emitter and sensor. The concepts of robustness for the Hampel filter and skipped filter are combined with shrinkage for the positive blind minimax and Bayes shrinkage estimation. It is DeMiguel and Nogales: Portfolio Selection with Robust Estimation Article submitted to Operations Research; manuscript no. OPRE-2007-02-106 3 a value of h=10% is enough to make the median as efficient as the mean, while more sophisticated

In the last decades, robust estimation has been widely applied to overcome the presence of gross errors in observations. Recently it has been shown that robust estimation, if computed appropriately, is able to cope with a larger amount of gross errors and also capable of providing reliable estimations in situations where systematic errors are present. It is the purpose of this paper to propose Some Contributions to Robust Inference for Discrete explicitly treated robust estimation for discrete data, although in prin-cip1e existing techniques can be used. One technique is to modify the maximum likelihood estimator in the following way. Replace the likelihood score in the estimating equation by a suitable bounded score functionljJ to limit the effect that an indivi-dual

The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down, that is, to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the finite sample as well as the asymptotic breakdown Package ‘ROptEstOld’ August 3, 2018 Version 1.1.0 Date 2018-08-01 Title Optimally Robust Estimation - Old Version Description Optimally robust estimation using S4 classes and methods.

Package ‘ROptEstOld’ August 3, 2018 Version 1.1.0 Date 2018-08-01 Title Optimally Robust Estimation - Old Version Description Optimally robust estimation using S4 classes and methods. The primary goal of robust statistics is the development of procedures which are still reliable and reasonably efficient under small deviations from the model, i.e. when the underlying distribution lies in a neighborhood of the assumed model. Robust statistics is then an extension of parametric

pdf hampel contributions to the theory of robust estimation

The goal of this PhD Thesis is the definition of new robust estimators, thereby extending the available theory and exploring new directions for applications in finance. The Thesis contains three papers, which analyze three different types of estimators: M-, Minimum Distance- and R- estimators. The Since the classical estimation and testing procedures are not robust with respect to deviations from the assumed underlying stochastic model, we propose in Section 3 new robust estimators and a new robust test for SSB, which are the natural robust counterparts of the classical Heck-