A PERMUTATION-BASED ESTIMATOR FOR MONOTONE INDEX MODELS
提出一种通过最小化排序数据相邻观测值距离来估计单调指数模型有限维参数的方法，无需选择带宽，估计量具有√n一致性和渐近正态性，蒙特卡洛模拟显示其均方误差和平均绝对偏差优于现有单调秩估计量。
This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data. The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized (over all possible permutations) when the observations are sorted by their values. The resulting estimator is a generalization of Cavanagh and Sherman's monotone rank estimator (MRE) (Cavanagh and Sherman, 1998, Journal of Econometrics 84, 351–381) and does not require a bandwidth choice. The estimator is $\sqrt{n}$ -consistent and asymptotically normal with a consistently estimable covariance matrix. This least-squares estimator can also be used to estimate monotone-index panel data models. A Monte Carlo study is presented where the proposed estimator is seen to dominate the MRE in terms of mean-squared error and mean absolute deviation.