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.
Poverty analysis often results in the computation of poverty indexes based on so-called poverty lines which can be region speci…c poverty lines. The poverty lines are made of two components, namely the amount of income to satisfy the food and the non food needs. For both components, one needs to estimate quantities such as local prices or the consummers' average basket, and this is often done through a parametric model. The resulting estimates depend on the data at hand and on the type of estimators that are used. Classical estimators (and testing procedures) such as the maximumlikelihood estimator (MLE) or the least squares (LS) estimator are extremely sensitive to model deviations such as contamination in the data and hence are said not robust. The resulting analysis can therefore give a picture which is far from reality. Therefore a robust statistical approach to the estimation of the poverty lines is very important especially because these lines will serve to compute poverty indices. The main purpose of this paper is therefore to show how robust statistical procedure can be used in poverty analysis and the di¤erent picture on poverty comparisons they can give to the Tunisian case.
Income distribution embeds a large field of research subjects in economics. It is important to study how incomes are distributed among the members of a population in order for example to determine tax policies for redistribution to decrease inequality, or to implement social policies to reduce poverty. The available data come mostly from surveys (and not censuses as it is often believed) and are often subject to long debates about their reliability because the sources of errors are numerous. Moreover the forms in which the data are available is not always as one would expect, i.e. complete and continuous (micro data) but one also can only have data in a grouped form (in income classes) and/or truncated data where a portion of the original data has been omitted from the sample or simply not recorded. Because of these data features, it is important to complement classical statistical procedures with robust ones. In this paper such methods are presented, especially for model selection, model fitting with several types of data, inequality and poverty analysis and ordering tools. The approach is based on the Influence Function (IF ) developed by Hampel (1974) and further developed by Hampel, Ronchetti, Rousseeuw, and Stahel (1986). It is also shown through the analysis of real UK and Tunisian data, that robust techniques can give another picture of income distribution, inequality or poverty when compared to classical ones.
En finance, le but d'un investisseur confronté à une construction de portefeuille est de trouver quelle combinaison d'actifs produira, dans le futur, le meilleur rendement possible, et cela pour un risque donné.
Successful estimation of the Pareto tail index from extreme order statistics relies heavily on the procedure used to determine the number of extreme order statistics that are used for the estimation. Most of the known procedures are based on the minimization of (an estimate of) the asymptotic mean square error of the Hill estimator for the Pareto tail index. The principal drawback of these approaches is that they involve the estimation of nuisance parameters, and therefore lead to complicated selection procedures. Instead, we propose to use Pareto quantile plots and build a prediction error estimator. The latter depends on the quantile at which the data are truncated, and it is minimized to find the optimal number of extreme order statistics used for estimating the Pareto tail index. The main advantages of the new approach are computational simplicity and the absence of estimation of nuisance parameters. The prediction error estimator is actually a generalization of Mallows' Cp to non-normal regression models. Through a simulation study involving several data generating models, we show that our prediction error criterion performs very well in terms of MSE compared to other procedures. The proposed method is also successfully applied to alluvial diamond deposits, finance,income, and insurance data.
Structural equation models have been around for now a long time. They are intensively used to analyze data from di.erent fields such as psychology, social sciences, economics, management, etc. Their estimation can be performed using standard statistical packages such as LISREL. However, these implementations su.er from an important drawback: they are not suited for cases in which the variables are far from the normal distribution. This happens in particular with ordinal data that have a non symmetric distribution, a situation often encountered in practice. An alternative approach would be to use generalized linear latent variable models (GLLVM) as defined for example in Bartholomew and Knott 1999 and Moustaki and Knott (2000). These models consider the data as they are, i.e. binary or ordinal but the loglikelihood function is intractable and needs numerical approximations to compute it. Several approaches exist such as Gauss-Hermite quadratures or simulation based methods, as well as the Laplace approximation, i.e. the Laplace approximated maximum likelihood estimator (LAMLE) proposed by Huber, Ronchetti, and Victoria-Feser (2004) for these models. The advantage of the later is that it is very fast and hence can cope with relatively complicated models. In this paper, we perform a simulation study to compare the parameters' estimators provided by LISREL which is taken as a benchmark, and the LAMLE when the data are generated from a confirmatory factor analysis model with normal variables which are then transformed into ordinal ones. We will show that while the LISREL estimators can provide seriously biased estimators, the LAMLE not only is unbiased, but one can also recover an unbiased estimator of the correlation matrix of the original normal variables.
In this paper we develop a structural equation model with latent variables in an ordinal setting which allows us to test broker-dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. An empirical illustration is given for mid-term forcasts simultaneously made by two broker-dealers for several countries.
This paper compares alternative methods of controlling for the spatial dependence of house prices in a mass appraisal context. Explicit modeling of the error structure is characterized as a relatively fluid approach to defining housing submarkets. This approach allows the relevant submarket to vary from house to house and for transactions involving other dwellings in each submarket to have varying impacts depending on distance. We conclude that "for our Auckland, New Zealand, data“ the gains in accuracy from including submarket variables in an ordinary least squares specification are greater than any benefits from using geostatistical or lattice methods. This conclusion is of practical importance, as a hedonic model with submarket dummy variables is substantially easier to implement than spatial statistical methods.
We analyze the impacts of alternative submarket definitions when predicting house prices in a mass appraisal context, using both ordinary least squares (OLS) and geostatistical techniques. For this purpose, we use over 13,000 housing transactions for Louisville, Kentucky. We use districts defined by the local property tax assessment office as well as a classification of census tracts generated by principal components and cluster analysis. We also experiment with varying numbers of census tract groupings. Our results indicate that somewhat better results are obtained with more homogeneous submarkets. Also, the accuracy of house price predictions increases as the number of submarkets is increased, but then quickly levels off. Adding submarket variables to the OLS model yields price predictions that are as accurate as when geostatistical methods are used to account for spatial dependence in the error terms. However, using both dummy variables for submarkets and geostatistical methods leads to significant increases in accuracy.
