Asymptotic Normality in a Semiparametric Regression Model

Suppase that y_i = x_iβ+g（x_i）+ε_i,1≤i≤n, where x_i are independent identically distributed （i.i.d） random samples with known variance σ₁², the ε_i are independent identically distributed random variables with zero means and finite variance σ²,β,g and the density function of ε_i are unknow. An estimator of β is constructed, whose variance is smaller than those given by other authors.