JSM 2005 Online Program

Abstract #304498

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Activity Number:	101
Type:	Contributed
Date/Time:	Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Business and Economics Statistics Section
Abstract - #304498
Title:	Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures
Author(s):	Mame Astou Diouf*+ and Jean-Marie Dufour
Companies:	University of Montreal and University of Montreal
Address:	4865 Queen Mary apt 8, Montreal, QC, H3W 1X1, Canada
Keywords:	poverty measures ; non parametric inference ; finite distance inference
Abstract:	We propose a finite sample nonparametric inference for Foster, Greer, and Thorbecke (FGT) poverty measures. Our inference relies on noting that FGT poverty measures are the expectation of bounded random variables. Then, following the result of Bahadur and Savage (1956), one could think the problem we try to solve has no solution, but we show it does. We first use a result of Anderson (1969) to show that confidence intervals for the mean of a continuous bounded random variable can be obtained by projection of Kolmogorov Smirnov confidence limits of the variable's cumulative distribution. Then, we apply this procedure to FGT measures defined as the mean of a mixing between a continuous bounded random variable and a mass at the poverty line. Simulations show that the confidence intervals we get are much better than asymptotic and bootstrap ones. The level of our confidence interval is closed to 100%, but has a larger interval range. Second, we improve the confidence interval using standardized Kolmogorov statistics. We derive a nonuniform confidence interval for distribution functions we project in the space of expectations.

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