This paper investigates model risk issues in the context of mean-variance portfolio selection. We analytically and numerically show that, under model misspecification, the use of statistically robust estimates instead of the widely used classical sample mean and covariance is highly beneficial for the stability properties of the mean-variance optimal portfolios. Moreover, we perform simulations leading to the conclusion that, under classical estimation, model risk bias dominates estimation risk bias. Finally, we suggest a diagnostic tool to warn the analyst of the presence of extreme returns that have an abnormally large influence on the optimization results.
With income distributions it is common to encounter the problem of missing data. When a parametric model is fitted to the data, the problem can be overcome by specifying the marginal distribution of the observed data. With classical methods of estimation such as the maximum likelihood (ML) an estimator of the parameters can be obtained in a straightforward manner. Unfortunately, it is well known that ML estimators are not robust estimators in the presence of contaminated data. In this paper, we propose a robust alternative to the ML estimator with truncated data, namely one based on Mestimators that we call the EMM estimator. We present an extensive simulation study where the EMM estimator based on optimal B-robust estimators (OBRE) is compared to a more conservative approach based on marginal density (MD) for truncated data, and show that the difference lies in the way the weights associated to each observation are computed. Finally, we also compare the EMM estimator based on the OBRE with the classical ML estimator when the data are contaminated, and show that contrary to the former, the latter can be seriously biased.
Distributional dominance criteria are commonly applied to draw welfare inferences about comparisons, but conclusions drawn from empirical implementations of dominance criteria may be inßuenced by data contamination. We examine a non-parametric approach to reÞning Lorenz-type comparisons and apply the technique to two important examples from the LIS data-base.
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 analytically by means of the Influence Function (IF) and empirically by means of simulations. 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 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 and they are applied to the analysis of binary data from a study on breastfeeding.
We show how a collection of results in the literature on the empirical estimation of welfare indicators from sample data can be unified. We also demonstrate how some of these ideas can be extended to empirically important cases where the data have been trimmed or censored.
Lorenz curves and associated tools for ranking income distributions are commonly estimated on the assumption that full, unbiased samples are available. However it is common to ¯nd income and wealth distributions that are routinely censored or trimmed. We derive the sampling distribution for a key family of statistics in the case where data have been modified in this fashion.
This paper presents a robust estimation of two income distribution models using Spanish data for the period 1990-91 under three different concepts of income. The effect on the estimates of the Theil index due to the choice of the definition of income and of the estimation method is also analysed.
Drawing on recent work concerning the statistical robustness of inequality statistics we examine the sensitivity of poverty indices to data contamination using the concept of the influence function. We show that poverty and inequality indices have fundamentally different robustness properties, and demonstrate that an important commonly used subclass of poverty measures will be robust under data contamination. We investigate both the case where the poverty line is exogenously fixed and where it must be estimated from the data.
Inequality measures are often used fot summarise 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. We investigate this issue theoretically using a technique based on the influence function, and illustrate the magnitude of the effect using a simulation. We consider both direct nonparametric estimation from the sample, and indirect estimation using a parametric model. In the latter case we demonstratge the application of a robust estimation procedure.
