Maria-Pia Victoria-Feser

Robustness Properties of Inequality Measures

Inequality measures are often used to summarize information about empirical income distributions. However the resulting picture of the distribution and of changes in the distribution can be severely distorted if the data are contaminated. The nature of this distortion will in general depend upon the underlying properties of the inequality measure. This issue is investigated theoretically using a technique based on the influence function, and the magnitude of the effect is illustrated using a simulation. Both direct nonparametric estimation from the sample, and indirect estimation using a parametric model are considered; in the latter case the application of a robust estimation procedure is demonstrated. The results are applied to two micro-data examples. Copyright 1996 by The Econometric Society.

Poverty measurement with contaminated data: A robust approach

We examine the sensitivity of poverty indices to data contamination using the concept of the influence function, and demonstrate that an important commonly used subclass of poverty measures will be robust under data contamination. This is illustrated using simulations. In this respect poverty and inequality indices have fundamentally different robustness properties. We investigate both the case where the poverty line is exogenously fixed and where it must be estimated from the data.

Robust Methods for Personal-Income Distribution Models

Statistical problems in modelling personal-income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum-likelihood and least-squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation problems.

Welfare Rankings in the Presence of Contaminated Data

Stochastic dominance criteria are commonly used to draw welfare-theoretic inferences about comparisons of income distribution as well as ranking probability distributions in the analysis of choice under uncertainty. However, just as some measures of location and dispersion can be catastrophically sensitive to extreme values in the data it is also possible that conclusions drawn from empirical implementations of dominance criteria are unduly influenced by data contamination. We show the conditions under which this may occur for a number of standard dominance tools used in welfare analysis.

Wavelet-Variance-Based Estimation for Composite Stochastic Processes

This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-based WV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic errors parameters of the sum of three first order Gauss–Markov processes by means of a sample of over 800, 000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online.

High‐breakdown estimation of multivariate mean and covariance with missing observations

We consider the problem of outliers in incomplete multivariate data when the aim is to estimate a measure of mean and covariance, as is the case, for example, in factor analysis. The ER algorithm of Little and Smith which combines the EM algorithm for missing data and a robust estimation step based on an M-estimator could be used in such a situation. 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 so-called high-breakdown estimator as the 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 estimator and the t-biweight S-estimator. Simulated and real data are used to compare and illustrate the different procedures.

Bounded-Influence Robust Estimation in Generalized Linear Latent Variable Models

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.

Distributional Dominance with Trimmed Data

Distributional dominance criteria are commonly applied to draw welfare inferences about comparisons, but conclusions drawn from empirical implementations of dominance criteria may be influenced by data contamination. We examine a nonparametric approach to refining Lorenz-type comparisons and apply the technique to two important examples from the Luxembourg Income Study database.

Generalized method of wavelet moments for inertial navigation filter design

The integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter calibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.

Robust Inference with Binary Data

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 Raos score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassifications 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.