Finite Sample Inference for the Maximum Score Estimand
针对Manski半参数二元响应模型，在条件中位数约束下，利用外生变量序列的条件矩不等式构造检验统计量，无需立方根渐近近似，通过已知函数的分位数进行推断，模拟和交通选择应用显示其有限样本性能优于现有方法。
Abstract We provide a finite sample inference method for the structural parameters of Manski's semiparametric binary response model under a conditional median restriction. This is achieved by exploiting distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on the size n sequence of exogenous covariates are constructed, and the proposed test statistic is a monotone function of violations of the corresponding sample moment inequalities. The critical value used for inference is provided by the appropriate quantile of a known function of n independent Bernoulli random variables and does not require the use of a cube root asymptotic approximation employing a point estimator of the target parameter. Simulation studies demonstrate favourable finite sample performance of the test in comparison to several existing approaches. Empirical use is illustrated with an application to the classical setting of transportation choice.