摘要翻译：
我们提出了一种基于Bootstrap的标定投影方法来建立单分量的置信区间和矩（in）等式模型中部分辨识参数向量的光滑函数的置信区间。该方法在一大类数据生成过程中统一控制渐近覆盖。标定投影置信区间的极值点是通过在适当松弛所研究的矩（in）等式条件下，对感兴趣函数值进行极值化而得到的。松弛的程度，或临界水平，被校准，使θ的函数，而不是θ本身，一致地渐近地被预先确定的概率覆盖。这种校准是基于反复检查线性规划问题的可行性，使其具有计算吸引力。然而，定义置信区间极值点的程序通常是非线性的，并且可能是复杂的。提出了一种基于响应面法的全局优化算法，该算法能快速准确地逼近解，并建立了其收敛速度。该算法适用于目标简单、约束复杂的优化问题。通过对一个进入博弈的实证应用，说明了该方法的有效性。Monte Carlo仿真验证了该算法的准确性，标定投影具有良好的统计性能和计算性能（包括与其他方法的比较），以及该算法大大加快其他置信区间计算的潜力。
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英文标题：
《Confidence Intervals for Projections of Partially Identified Parameters》
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作者：
Hiroaki Kaido and Francesca Molinari and J\"org Stoye
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of theta, not theta itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive.   Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.
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PDF链接：
https://arxiv.org/pdf/1601.00934