Robust Lorenz Curves: A Semiparametric Approach

Lorenz curves and second-order dominance criteria are known to be sensitive to data contamination in the right tail of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models for income distributions, and (2) Combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust approach (2). Statistical inference tools are also provided.Welfare dominance, Lorenz curve, Pareto model, M-estimators.

Distributional Dominance with Dirty 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 non-parametric approach to refining Lorenz-type comparisons and apply the technique to two important examples from the LIS data-base.Distributional dominance, Lorenz curve, robustness.

Statistical Inference for Lorenz Curves with Censored Data

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 find 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.Lorenz curve, sampling errors

Modelling Lorenz Curves:robust and semi-parametric issues

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distribution. It is conventional to use non-parametric statistics based on empirical income cumulants which are in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to 'wrong' interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the datagenerating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser 2002), trimmed LC (Cowell and Victoria-Feser 2006) and inference for trimmed LC (Cowell and Victoria-Feser 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser 2007) selection of optimal thresholds for (robust) semi parametric modelling (Dupuis and Victoria-Feser 2006) and use both simulations and real data to illustrate these points.

Robustness Properties of Inequality Measures: The Influence Function and the Principle of Transfers (Revised version in Economica, 64 (1996), pp.77-101)

Inequality measures are often used to summarise information about empirical income distributions. However , the resulting picture of the distribution and of the 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 the indirect estimation using a parametric model; in the latter case we demonstrate the application of a robust estimation procedure.Inequality measurement, transfer principle, influence function, robust estimation

Heightened Levels of Antimicrobial Response Factors in Patients With Rheumatoid Arthritis

Rheumatoid arthritis (RA) is a chronic progressive autoimmune disease leading to considerable disability over time. The disease can be characterized by the presence of multiple autoantibodies in the serum and synovial fluid. Microbial dysbiosis is proposed to play a role in the pathogenesis of RA. Increased systemic bacterial exposure leads to elevated levels of antimicrobial response factors (ARFs) in the circulation. In the present study, we tested whether RA patients have increased levels of ARFs by analyzing the levels of multiple ARFs in serum from RA patients and healthy age and sex-matched controls. The levels of soluble CD14 (sCD14), lysozyme, and CXCL16 were significantly elevated in RA patients compared to healthy controls. Lipopolysaccharide binding protein (LBP) levels remained unchanged in RA patients compared to healthy controls. A positive correlation of LBP with rheumatoid factor (RF) was also found in RA subjects. Interestingly, the levels of anti-endotoxin core antibodies (EndoCAb) IgM, total IgM, EndoCAb IgA, and total IgA were significantly elevated in RA patients compared to healthy controls. No significant changes in the levels of EndoCAb IgG and total IgG were observed in RA patients compared to healthy controls. Furthermore, lysozyme and CXCL16 levels were positively correlated with disease severity among RA subjects. Increases in the levels of several ARFs and their correlations with clinical indices suggest systemic microbial exposure in the RA cohort. Modulation of microbial exposure may play an important role in disease pathogenesis in individuals with RA

Analyzing the causes and spatial pattern of the European 2003 carbon flux anomaly using seven models

Globally, the year 2003 is associated with one of the largest atmospheric CO<sub>2</sub> rises on record. In the same year, Europe experienced an anomalously strong flux of CO<sub>2</sub> from the land to the atmosphere associated with an exceptionally dry and hot summer in Western and Central Europe. In this study we analyze the magnitude of this carbon flux anomaly and key driving ecosystem processes using simulations of seven terrestrial ecosystem models of different complexity and types (process-oriented and diagnostic). We address the following questions: (1) how large were deviations in the net European carbon flux in 2003 relative to a short-term baseline (1998–2002) and to longer-term variations in annual fluxes (1980 to 2005), (2) which European regions exhibited the largest changes in carbon fluxes during the growing season 2003, and (3) which ecosystem processes controlled the carbon balance anomaly . <br><br> In most models the prominence of 2003 anomaly in carbon fluxes declined with lengthening of the reference period from one year to 16 years. The 2003 anomaly for annual net carbon fluxes ranged between 0.35 and –0.63 Pg C for a reference period of one year and between 0.17 and –0.37 Pg C for a reference period of 16 years for the whole Europe. <br><br> In Western and Central Europe, the anomaly in simulated net ecosystem productivity (NEP) over the growing season in 2003 was outside the 1σ variance bound of the carbon flux anomalies for 1980–2005 in all models. The estimated anomaly in net carbon flux ranged between –42 and –158 Tg C for Western Europe and between 24 and –129 Tg C for Central Europe depending on the model used. All models responded to a dipole pattern of the climate anomaly in 2003. In Western and Central Europe NEP was reduced due to heat and drought. In contrast, lower than normal temperatures and higher air humidity decreased NEP over Northeastern Europe. While models agree on the sign of changes in simulated NEP and gross primary productivity in 2003 over Western and Central Europe, models diverge in the estimates of anomalies in ecosystem respiration. Except for two process models which simulate respiration increase, most models simulated a decrease in ecosystem respiration in 2003. The diagnostic models showed a weaker decrease in ecosystem respiration than the process-oriented models. Based on the multi-model simulations we estimated the total carbon flux anomaly over the 2003 growing season in Europe to range between –0.02 and –0.27 Pg C relative to the net carbon flux in 1998–2002

Analyzing the causes and spatial pattern of the European 2003 carbon flux anomaly using seven models

Globally, the year 2003 is associated with one of the largest atmospheric CO2 rises on record. In the same year, Europe experienced an anomalously strong flux of CO2 from the land to the atmosphere associated with an exceptionally dry and hot summer in Western and Central Europe. In this study we analyze the magnitude of this carbon flux anomaly and key driving ecosystem processes using simulations of seven terrestrial ecosystem models of different complexity and types (process-oriented and diagnostic). We address the following questions: (1) how large were deviations in the net European carbon flux in 2003 relative to a short-term baseline (1998–2002) and to longer-term variations in annual fluxes (1980 to 2005), (2) which European regions exhibited the largest changes in carbon fluxes during the growing season 2003, and (3) which ecosystem processes controlled the carbon balance anomaly . In most models the prominence of 2003 anomaly in carbon fluxes declined with lengthening of the reference period from one year to 16 years. The 2003 anomaly for annual net carbon fluxes ranged between 0.35 and –0.63 Pg C for a reference period of one year and between 0.17 and –0.37 Pg C for a reference period of 16 years for the whole Europe. In Western and Central Europe, the anomaly in simulated net ecosystem productivity (NEP) over the growing season in 2003 was outside the 1σ variance bound of the carbon flux anomalies for 1980–2005 in all models. The estimated anomaly in net carbon flux ranged between –42 and –158 Tg C for Western Europe and between 24 and –129 Tg C for Central Europe depending on the model used. All models responded to a dipole pattern of the climate anomaly in 2003. In Western and Central Europe NEP was reduced due to heat and drought. In contrast, lower than normal temperatures and higher air humidity decreased NEP over Northeastern Europe. While models agree on the sign of changes in simulated NEP and gross primary productivity in 2003 over Western and Central Europe, models diverge in the estimates of anomalies in ecosystem respiration. Except for two process models which simulate respiration increase, most models simulated a decrease in ecosystem respiration in 2003. The diagnostic models showed a weaker decrease in ecosystem respiration than the process-oriented models. Based on the multi-model simulations we estimated the total carbon flux anomaly over the 2003 growing season in Europe to range between –0.02 and –0.27 Pg C relative to the net carbon flux in 1998–2002

Impact Forecasting to Support Emergency Management of Natural Hazards

Forecasting and early warning systems are important investments to protect lives, properties, and livelihood. While early warning systems are frequently used to predict the magnitude, location, and timing of potentially damaging events, these systems rarely provide impact estimates, such as the expected amount and distribution of physical damage, human consequences, disruption of services, or financial loss. Complementing early warning systems with impact forecasts has a twofold advantage: It would provide decision makers with richer information to take informed decisions about emergency measures and focus the attention of different disciplines on a common target. This would allow capitalizing on synergies between different disciplines and boosting the development of multihazard early warning systems. This review discusses the state of the art in impact forecasting for a wide range of natural hazards. We outline the added value of impact-based warnings compared to hazard forecasting for the emergency phase, indicate challenges and pitfalls, and synthesize the review results across hazard types most relevant for Europe