Confidence Intervals for Projections of Partially Identified Parameters
Confidence Intervals for Projections of Partially Identified Parameters
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DOI：
10.3982/ecta14075
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发表时间：
2019-07-01
期刊：
影响因子：
6.1
通讯作者：
Stoye, Jorg
中科院分区：
文献类型：
--
作者：
Kaido, Hiroaki;Molinari, Francesca;Stoye, Jorg
我们提出了一种基于Bootstrap的校正投影过程来为矩(In)相等模型中的单个分量和部分识别的参数向量的光滑函数建立置信度区间。该方法在一大类数据生成过程上一致地控制渐近覆盖。校准的投影可信区间的极值点是通过使感兴趣函数的值取极值来获得的，该值服从于矩(在)相等条件下的学生化样本类比的适当放宽。松弛程度，或临界水平，被校准，以便以预先指定的概率一致地渐进地覆盖theta的函数，而不是theta本身。这种校准是基于反复检查线性规划问题的可行性，使其在计算上具有吸引力。尽管如此，定义置信度区间极值点的程序通常是非线性的，而且可能是复杂的。基于全局优化的响应面方法，给出了一种快速、准确地逼近解的算法，并建立了它的收敛速度。该算法对具有简单目标和复杂约束的优化问题具有独立的意义。一个估计进入博弈的实证应用说明了该方法的有效性。蒙特卡罗模拟证实了该算法的准确性，校准投影的良好的统计和计算性能(包括与其他方法相比)，以及该算法极大地加速其他置信度区间的计算的潜力。
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.