Inference for the Mean

均值推断

• 批准号: 1919336
• 负责人: Ulrich Mueller
• 金额: $ 18.45万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-15 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1919336&HistoricalAwards=false
• 关键词: Inference; Mean

A key challenge of drawing conclusions about a population from a sample of individuals is how to accurately describe the uncertainty about the population average because one only observes a sample, rather than the whole population. The standard approach relies on approximating the distribution of the sample average by a bell-shaped distribution, whose spread can be estimated by the variability of the sample observations. When the underlying population distribution is not bell shaped, this approximation becomes poor in small samples, leading to a wrong representation of the uncertainty about the population average. This proposal will develop a new method for describing the uncertainty that remains accurate even for non-bell-shaped populations. This is done by modelling the potentially non-bell-shaped structure in the construction of the uncertainty estimate. More complicated problems of drawing conclusions can be cast into drawing conclusions about the average of a suitably defined population. The results of this research could thus have many practical applications in the social sciences and improve business and policy decision making. The end results are to increase economic efficiency and speed up economic growth. This proposal seeks to develop an alternative to standard t-statistic-based inference about the mean from a sample of i.i.d. observations that better controls size for moderately heavy-tailed underlying populations. It combines extreme value theory for the k smallest and k largest observations with a normal approximation for the average of the remaining middle n-2k observations. The mean shift is a function of the same tail parameters that govern the extreme value distributions, as well as the realized value of the extreme observations. One thus obtains an approximate parametric model for 2k+1 observation, with the tail parameters as nuisance parameters; one can apply numerical techniques to obtain valid and powerful test in this approximate parametric model. The main theoretical result shows that this approach represents an improvement over existing method. For populations with finite variance but infinite third moment, the new approach induces smaller errors in rejection probability compared to the usual t-statistic, or the percentile-t bootstrap, at least as long as the population is such that extreme value theory provides accurate approximations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

从个体样本中得出总体结论的一个关键挑战是如何准确描述总体平均值的不确定性，因为人们只观察样本，而不是整个总体。标准方法依赖于通过钟形分布来近似样本平均值的分布，其分布可以通过样本观察的变异性来估计。当基础总体分布不是钟形时，这种近似在小样本中会变得很差，从而导致对总体平均值的不确定性的错误表示。该提案将开发一种新的方法来描述不确定性，即使对于非钟形群体也仍然准确。这是通过在构建不确定性估计时对潜在的非钟形结构进行建模来完成的。更复杂的得出结论的问题可以归结为对适当定义的总体的平均值得出结论。因此，这项研究的结果可以在社会科学领域有许多实际应用，并改善商业和政策决策。最终结果是提高经济效率并加快经济增长。该提案旨在开发一种替代方法，以替代基于标准 t 统计量的 i.i.d. 样本平均值推断。更好地控制中等重尾基础种群大小的观察结果。它将 k 个最小和 k 个最大观测值的极值理论与剩余中间 n-2k 个观测值的平均值的正态近似相结合。均值漂移是控制极值分布的相同尾部参数以及极端观测值的实现值的函数。由此得到2k+1次观测的近似参数模型，其中尾部参数为干扰参数；人们可以应用数值技术在这个近似参数模型中获得有效且有力的检验。主要理论结果表明该方法是对现有方法的改进。对于方差有限但三阶矩无限的群体，与通常的 t 统计量或百分位数 t 自举法相比，新方法在拒绝概率上产生的误差更小，至少只要群体能够使极值理论提供准确的近似值。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Spatial Correlation Robust Inference

空间相关性鲁棒推理

• DOI: 10.3982/ecta19465
• 发表时间: 2022
• 期刊: Econometrica
• 影响因子: 6.1
• 作者: Müller, Ulrich K.;Watson, Mark W.
• 通讯作者: Watson, Mark W.

An Econometric Model of International Growth Dynamics for Long-horizon Forecasting

用于长期预测的国际增长动态计量经济学模型

• 发表时间: 2022
• 期刊: The review of economics and statistics
• 作者: Ulrich K. Müller, James H.