Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures
Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures
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改进有界随机变量均值的非参数推断并应用于贫困测量
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发表时间：
2005
期刊：
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通讯作者：
Jean
中科院分区：
文献类型：
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作者：
Mame Astou Diouf;Jean
我们为有界随机变量的均值提供新的有限样本非参数推理方法。为此，我们证明巴哈杜尔和萨维奇（1956）的不可能性定理在这种情况下不适用。接下来，我们观察到有界随机变量均值的置信区间实际上可以通过从适当分布函数的置信区间投影来导出，并研究基于改进的 Kolmogorov Smirnov 统计和似然比改进的有限样本非参数方法。此外，我们将所有研究的推理方法应用于 Foster、Greer 和 Thorbecke（FGT，1984）贫困指标。我们证明，FGT 贫困指标实际上是对一些有界随机变量的期望，即连续有界随机变量与贫困线处的质量之间的混合。因此，所有有界随机变量均值的推断方法都适用于这种情况。我们研究这些方法的相对性能。蒙特卡罗模拟证明了使用有限样本非参数方法的必要性。渐近和自举推理方法在有限样本中显得不可靠。相反，我们提出的有限样本非参数推理方法对于我们使用的框架和样本量来说是鲁棒的。我们得到的置信区间具有非常好的覆盖概率（始终接近 100%）和良好的精度。此外，我们提供显式表达式，这使得它们非常容易计算。
We provide new finite sample nonparametric inference methods for the mean of a bounded random variable. For this purpose, we prove that the impossibility theorem of Bahadur and Savage (1956) does not apply in this case. Next, we observe that confidence intervals for the mean of a bounded random variable can actually be derived by projection from confidence intervals for the adequate distribution function and investigate finite sample nonparametric methods based on improved Kolmogorov Smirnov statistics and likelihood ratio improvement. Further, we apply all studied inference methods on the Foster, Greer and Thorbecke (FGT, 1984) poverty measures. We show that FGT poverty measures are actually expectations of some bounded random variables, namely a mixing between a continuous bounded random variable and a mass at the poverty line. So, all inference methods for the mean of bounded random variable apply to this case. We study the relative performance of such methods. Monte Carlo simulations demonstrate the necessity of using finite sample nonparametric approaches. The asymptotic and bootstrap inference methods appear not reliable in finite sample. On the contrary, the finite sample nonparametric inference methods we propose are robust to the framework and the sample size we use. Confidence intervals we get have a very good coverage probability (always close to 100%) and a good precision. In addition, we provide explicit expressions which make them very easy to compute.