Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors
研究当解释变量是未知条件均值时，如何用两步法估计单指数模型参数，第一步非参数估计条件均值，第二步用加权平均导数法估计参数，并证明估计量的一致性和渐近正态性。
This paper develops a theory of estimating parameters of a generated regressor model in which some explanatory variables in the equation of interest are the unknown conditional means of certain observable variables given other observable regressors. The paper imposes a weak nonparametric restriction on the form of the conditional means and maintains a single-index assumption on the distribution of the dependent variable in the equation of interest. The estimation method follows a two-step approach: The first step estimates the conditional means in the index nonparametrically, and the second step estimates the parameters by an analytically convenient weighted average derivative method. It is established that the two-step estimator is root- n -consistent and asymptotically normal. The asymptotic variance exceeds that of the one-step hypothetical estimator, which would be obtainable if the first-step regression were known.