Uniform asymptotics for robust location estimates when the scale is unknown

Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000054

Robust nonparametric inference for the median

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some measures of robustness and efficiency under contamination for confidence intervals and tests. These measures are computed for the proposed procedures.Comment: Published at http://dx.doi.org/10.1214/009053604000000634 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Poverty Targeting, Resource Degradation and Heterogeneous Endowments A Micro-Simulation Analysis of a Less Favored Ethiopian Village

Persistent and widespread poverty in less favored areas (LFAs) is attributed to fragile natural resources and poor markets. Limited assets may keep households outside the reach of poverty policies targeted at LFAs. We explore in a stylized manner the role of heterogeneous household assets for (1) policies aimed at poverty reduction; (2) within-village income inequality; (3) soil erosion. With a farm-household microsimulation model we analyze for each household in a remote Ethiopian village three sets of policies: technology improvement, infrastructure investment, and off-farm employment through migration or cash for work (CFW) programs. Combating poverty with a single policy, migration reduces the poverty headcount most. Because of self-selection, CFW programs performed best in terms of reaching the poorest of the poor. CFW also reduce within-village income inequality most, while a price band reduction increases income inequality. Only technology improvements imply a trade-off between poverty and soil erosion. Price band and off-farm employment reduce erosion while outperforming technology improvements in terms of poverty reduction. Combining two policies helps poorer households to overcome the limitations of their asset endowments. Combining a cash for work program with a reduction in price bands yields most in terms of poverty reduction and income inequality. This policy complementarity is less important for better endowed households. Reducing the reliance of households on agriculture offers a winwin situation of reducing poverty and maintaining natural resources. Combining policies helps to overcome asset limitations, to target policies to the poorest households and to reduce income inequalities.less-favored areas, farm households, poverty, erosion, micro-simulation, Ethiopia, Food Security and Poverty, Resource /Energy Economics and Policy, C6, Q12, Q56,