We review the use and the interpretation of some robustness concepts and techniques in some economic applications. We focus on estimation techniques in income distribution analysis and we discuss the reliability of inequality measures.
In this paper we propose a robust version of Cox-type test statistics for the choice between two non-nested hypotheses. We first show that the influence of small amounts of contamination in the data on the test decision can be very large. Secondly we build a robust test statistic by using the results on robust parametric tests available in the literature and show that the level of the robust test is stable. Finally, we show numerically not only the good property of robustness of this new test statistic, but also that its asymptotic distribution is a good approximation of its sample distribution, unlike for the classical test statistic.
The paper discusses the effect of model deviations such as data contamination on the maximum likelihood estimator (MLE) for a general class of latent trait models (citeNP{MoKn:00}). This is done with the use of the influence function (Hampel 1968, 1974) a mathematical tool to assess the robustness properties of any statistic, such as an estimator. Simulation studies show that the MLE can be seriously biased by model deviations. Therefore, we then propose alternative robust estimators that are not less influenced by data contamination. The performance of the robust estimators in terms of bias and variance is compared to the MLE estimator both analytically and through simulation studies.
Latent variable models are used for analyzing multivariate data. Recently, generalized linear latent variable models for categorical, metric, and mixed-type responses estimated via maximum likelihood (ML) have been proposed. Model deviations, such as data contamination, are shown analytically, using the influence function and through a simulation study, to seriously affect ML estimation. This article proposes a robust estimator that is made consistent using the basic principle of indirect inference and can be easily numerically implemented. The performance of the robust estimator is significantly better than that of the ML estimators in terms of both bias and variance. A real example from a consumption survey is used to highlight the consequences in practice of the choice of the estimator.
The data available for estimating welfare indicators are often inconveniently incomplete data: they may be censored or truncated. Furthermore, for robustness reasons, researchers sometimes use trimmed samples. By using the statistical tool known as the Influence Function we derive distribution-free asymptotic variances for wide classes of welfare indicators not only in the complete data case, but also in the important cases where the data have been trimmed, censored or truncated.
In this paper we study bias-corrections to the weighted MLE (Dupuis and Morgenthaler, 2002), a robust estimator simply defined through a weighted score function. Indeed, although the WMLE is relatively simple to compute, for most models it is not consistent and hence not very helpful. For example, the model we consider in this paper is the generalized linear latent variable model (GLLVM) proposed in Moustaki and Knott (2000) (see also Moustaki, 1996, Sammel, Ryan, and Legler, 1997 and Bartholomew and Knott, 1999). The score functions of this model are very complicated. They contain integrals that need to be evaluated. Moreover, they are highly nonlinear in the parameters which makes the use of complicated robust estimator quite impossible in practice. Moustaki and Victoria-Feser (2006) propose to use a weighted MLE and develop indirect inference (Gouri´eroux, Monfort, and Renault, 1993, Gallant and Tauchen, 1996 and also Genton and de Luna, 2000, Genton and Ronchetti, 2003) to remove the bias. It can be computed in a simple iterative fashion. In this paper, we actually focus on indirect inference for bias correction in general. We rely heavily on the findings of Moustaki and Victoria-Feser (2006).
In this paper robustness properties of the maximum likelihood estimator (MLE) and several robust estimators for the logistic regression model when the responses are binary are analysed. It is found that the MLE and the classical Rao's score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassification's errors in the responses, or extreme data points in the design space. A general framework for robust estimation and testing is presented and a robust estimator as well as a robust testing procedure are presented. It is shown that they are less influenced by model misspecifications than their classical counterparts. They are finally applied to the analysis of binary data from a study on breastfeeding.
In this paper, we consider the problem of outliers in incomplete multivariate data, when the aim is to estimate a measure of mean and covariance as it is the case for example in factor analysis. In such a situation the ER algorithm of Little and Smith (1987) which combines the EM algorithm for missing data and a robust estimation step based on an Mestimator could be used. However, the ER algorithm as originally proposed can fail to be robust in some cases especially in high dimensions. We propose here two alternatives to avoid the problem. One is to combine a small modification of the ER algorithm with a socalled high breakdown estimator as starting point for the iterative procedure and the other is to base the estimation step of the ER algorithm on a high breakdown estimator. Among the high breakdown estimators which are actually built to keep their robustness properties even if the number of variables is relatively large, we consider here the minimum covariance determinant (MCD) estimator and the t-biweight S-estimator. Simulated and real data are used to compare and illustrate the different procedures.
