Non‐standard rates of convergence of criterion‐function‐based set estimators for binary response models
研究了半参数二元响应模型在条件中位数约束下，基于准则函数等高线集合的估计量的一致性和非标准收敛速度，发现存在连续但有界回归变量时估计量以立方根速度收敛，所有回归变量离散时收敛速度可任意快，并验证了子抽样方法构建置信集的有效性。
This paper establishes consistency and non‐standard rates of convergence for set estimators based on contour sets of criterion functions for a semi‐parametric binary response model under a conditional median restriction. The model can be partially identified due to potentially limited‐support regressors and an unknown distribution of errors. A set estimator analogous to the maximum score estimator is essentially cube‐root consistent for the identified set when a continuous but possibly bounded regressor is present. Arbitrarily fast convergence occurs when all regressors are discrete. We also establish the validity of a subsampling procedure for constructing confidence sets for the identified set. As a technical contribution, we provide more convenient sufficient conditions on the underlying empirical processes for cube‐root convergence and a sufficient condition for arbitrarily fast convergence, both of which can be applied to other models. Finally, we carry out a series of Monte Carlo experiments, which verify our theoretical findings and shed light on the finite‐sample performance of the proposed procedures.