半参数单指标回归模型的估计及其强相合性

Estimators and strong consistency in a semiparametric single-index regression model

讨论了半参数单指标回归模型y=αTx+g(βTu)+ε,针对未知向量β,给出了一种不同于单指标投影追踪的估计方法,并证明了估计量α^n以及β^n具有强相合性,最后对所估计方法进行了模拟验证.

Respect to the unknown vector β,a new estimator which is different from the single-index projection pursuit estimator was presented specifically to slove the semiparametric single-index regression model y=αTx＋g（βTu）＋ε.The strong consistency of the estimators n,n were proved and the validation of the model was carried out by simulation.