Maximum score estimation with nonparametrically generated regressors
研究在不确定性下二元选择模型中偏好参数的两阶段最大得分估计，先非参数估计条件期望，再基于此估计偏好参数，并证明估计量的一致性和收敛速度。
The estimation problem in this paper is motivated by the maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages. We estimate conditional expectations nonparametrically in the first stage. Then, in the second stage, we estimate the preference parameters based on the maximum score estimator of Manski, using the choice data and first‐stage estimates. This setting can be extended to maximum score estimation with nonparametrically generated regressors. In this paper, we establish consistency and derive the rate of convergence of the two‐stage maximum score estimator. Moreover, we also provide sufficient conditions under which the two‐stage estimator is asymptotically equivalent in distribution to the corresponding single‐stage estimator that assumes the first‐stage input is known. We also present some Monte Carlo simulation results for the finite‐sample behaviour of the two‐stage estimator.