ESTIMATION OF DENSITY FUNCTION FOR SEMI-PARAMETRIC MODEL

Let X, X_1, \ldots, X_n be a sequence of iid K-dimensional random vectors with density function f(x) \epsilon \mathscrF \geqslant \boldsymbolS^-0=\left\f(x, \theta): \theta \in \Theta \subseteq R^p\right\ we have built an estimate for f(x) sach that it converges to f(x) almost surely whether the parametric model (f \in \mathcalF^0) or not and when f \in \mathcalF^0 it is better than the nonparametric estimate \hatf_n(x), we consider both the regularity case and the nonregularity case.