Simple Estimators for Invertible Index Models
提出一种估计线性指数系数的简单方法，适用于简化型参数多于指数个数的情形，估计量是某个矩阵的最小特征值对应的特征向量，且具有根n一致性和渐近正态性。
This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index coefficients (up to scale) is the eigenvector of a matrix (defined in terms of a first-step nonparametric estimator of the reduced form parameters) corresponding to its smallest (in magnitude) eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal, and under additional restrictions an efficient choice of a “weight matrix” is derived in the overdetermined case.